(* Content-type: application/vnd.wolfram.mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 10.3' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 158, 7] NotebookDataLength[ 559008, 13268] NotebookOptionsPosition[ 553852, 13096] NotebookOutlinePosition[ 554197, 13111] CellTagsIndexPosition[ 554154, 13108] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[CellGroupData[{ Cell["Section 2.5 Renyi entropy and entanglement entropy", "Section", CellChangeTimes->{{3.7039542022131257`*^9, 3.703954219345484*^9}, { 3.7039553305656457`*^9, 3.703955332918915*^9}, 3.7041728946630497`*^9, { 3.7118128680739017`*^9, 3.7118128958433123`*^9}, {3.7118129736796036`*^9, 3.7118129751449556`*^9}, {3.711813013890053*^9, 3.7118130186411047`*^9}}], Cell[CellGroupData[{ Cell["S_n(L,\[Phi]) and S(L,\[Phi])", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SnL\[Phi]", "=", RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"Log", "[", "\[ScriptL]", "]"}]}], RowBox[{"12", " ", "n"}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", SuperscriptBox["\[Pi]", "2"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "2"]}], RowBox[{"72", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "2"], " ", "n"}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["n", "2"]}], "-", RowBox[{"24", " ", "c", " ", "h\[Phi]", " ", RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"]}], ")"}]}], "+", RowBox[{"48", " ", SuperscriptBox["h\[Phi]", "2"], " ", RowBox[{"(", RowBox[{"11", "+", SuperscriptBox["n", "2"]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], RowBox[{"2160", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L", "4"], " ", SuperscriptBox["n", "3"]}], ")"}]}]], "-", RowBox[{ FractionBox["1", RowBox[{"34020", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L", "6"], " ", SuperscriptBox["n", "5"]}], ")"}]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"96", " ", SuperscriptBox["h\[Phi]", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"2", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"47", "+", SuperscriptBox["n", "2"]}], ")"}]}], "-", RowBox[{"24", " ", SuperscriptBox["c", "2"], " ", "h\[Phi]", " ", RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"], "+", SuperscriptBox["n", "4"]}], ")"}]}], "+", RowBox[{"36", " ", "c", " ", SuperscriptBox["h\[Phi]", "2"], " ", RowBox[{"(", RowBox[{"37", "+", RowBox[{"9", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["n", "4"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}]}], "-", RowBox[{ FractionBox["1", RowBox[{"453600", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "7"]}], ")"}]}]], RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", SuperscriptBox["c", "5"], " ", SuperscriptBox["n", "6"]}], "+", RowBox[{"5632", " ", SuperscriptBox["h\[Phi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "3"}], "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"2", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"3", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"119", "+", SuperscriptBox["n", "2"]}], ")"}]}], "+", RowBox[{"64", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["h\[Phi]", "2"], " ", RowBox[{"(", RowBox[{"1078", "-", RowBox[{"5863", " ", "h\[Phi]"}], "+", RowBox[{ RowBox[{"(", RowBox[{"268", "+", RowBox[{"1227", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["n", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"100", "+", RowBox[{"303", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["n", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"30", "+", RowBox[{"13", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["n", "6"]}]}], ")"}]}], "-", RowBox[{"2", " ", SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "11"}], " ", SuperscriptBox["n", "6"]}], "+", RowBox[{"60", " ", "h\[Phi]", " ", RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "4"]}], ")"}]}]}], ")"}]}], "+", RowBox[{"48", " ", SuperscriptBox["c", "3"], " ", "h\[Phi]", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "11"}], " ", RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "4"]}], ")"}]}], "+", RowBox[{"h\[Phi]", " ", RowBox[{"(", RowBox[{"251", "+", RowBox[{"71", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"29", " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"9", " ", SuperscriptBox["n", "6"]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"64", " ", "c", " ", SuperscriptBox["h\[Phi]", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "44"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2"}], "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"2", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"11", "+", SuperscriptBox["n", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"19", "+", SuperscriptBox["n", "2"]}], ")"}]}], "+", RowBox[{"h\[Phi]", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "58213"}], "+", RowBox[{"33927", " ", SuperscriptBox["n", "2"]}], "-", RowBox[{"1647", " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"13", " ", SuperscriptBox["n", "6"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"]}]}], ";"}]], "Input", CellChangeTimes->{{3.703954262836425*^9, 3.703954264976242*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SL\[Phi]", "=", InterpretationBox[ RowBox[{ RowBox[{ FractionBox["1", "6"], " ", "c", " ", RowBox[{"Log", "[", "\[ScriptL]", "]"}]}], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["\[Pi]", "2"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "2"]}], RowBox[{"36", " ", SuperscriptBox["L", "2"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], RowBox[{"1080", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L", "4"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], "3"], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], RowBox[{"17010", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L", "6"]}], ")"}]}]], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"96", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"1152", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"82", "+", RowBox[{"15", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "-", RowBox[{"92160", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"3", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}], "+", RowBox[{"184320", " ", RowBox[{"(", RowBox[{"88", "+", RowBox[{"9", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], ")"}], "/", RowBox[{"(", RowBox[{"226800", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"]}], ")"}]}], ")"}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 0, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, {(Rational[1, 6] $CellContext`c) Log[$CellContext`\[ScriptL]], 0, ((Rational[-1, 36] ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L^(-2)) Pi^2, 0, (((Rational[-1, 1080]/$CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi])^2) $CellContext`L^(-4)) Pi^4, 0, (((Rational[-1, 17010] $CellContext`c^(-2)) ($CellContext`c - 24 $CellContext`h\[Phi])^3) $CellContext`L^(-6)) Pi^6, 0, ((((Rational[-1, 226800] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) ($CellContext`c^4 (22 + 5 $CellContext`c) - (( 96 $CellContext`c^3) (22 + 5 $CellContext`c)) $CellContext`h\[Phi] + (( 1152 $CellContext`c^2) (82 + 15 $CellContext`c)) $CellContext`h\[Phi]^2 - (( 92160 $CellContext`c) (22 + 3 $CellContext`c)) $CellContext`h\[Phi]^3 + ( 184320 (88 + 9 $CellContext`c)) $CellContext`h\[Phi]^4)) $CellContext`L^(-8)) Pi^8}, 0, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.703954287541833*^9, 3.7039543162508936`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["S_n(L,q) and S(L,q)", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7039543262632046`*^9, 3.703954327394719*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SnLq", "=", RowBox[{"SnLLq", "+", "SnNLLq", "+", "SnNNLLq"}]}], ";"}]], "Input", CellChangeTimes->{{3.7039552026228957`*^9, 3.7039552209084463`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SnLLq", "=", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"Log", "[", "\[ScriptL]", "]"}]}], RowBox[{"12", " ", "n"}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"c", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", SuperscriptBox["\[Pi]", "2"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "2"]}], RowBox[{"72", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "2"], " ", "n"}], ")"}]}]], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"2160", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "4"], " ", "n"}], ")"}]}]]}], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"18", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "4"], " ", SuperscriptBox["n", "3"]}], ")"}]}]], "-", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"9", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "4"], " ", SuperscriptBox["n", "3"]}], ")"}]}]], "-", FractionBox[ RowBox[{"11", " ", RowBox[{"(", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"18", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "4"], " ", SuperscriptBox["n", "3"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[-1, 2160] $CellContext`c $CellContext`L^(-4) $CellContext`n^(-1) ( 1 + $CellContext`n) Pi^4, 0, Rational[-1, 18] $CellContext`c $CellContext`L^(-4) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^4, Rational[-2, 9] $CellContext`c $CellContext`L^(-4) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^4, Rational[-11, 18] $CellContext`c $CellContext`L^(-4) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^4}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"34020", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "6"], " ", "n"}], ")"}]}]]}], "+", FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "2"]}], RowBox[{"27", " ", SuperscriptBox["L", "6"], " ", SuperscriptBox["n", "3"]}]], "+", FractionBox[ RowBox[{"10", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "3"]}], RowBox[{"27", " ", SuperscriptBox["L", "6"], " ", SuperscriptBox["n", "3"]}]], "+", FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"1", "-", RowBox[{"49", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"48", " ", SuperscriptBox["n", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "4"]}], RowBox[{"27", " ", SuperscriptBox["L", "6"], " ", SuperscriptBox["n", "5"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[-1, 34020] $CellContext`c $CellContext`L^(-6) $CellContext`n^(-1) ( 1 + $CellContext`n) Pi^6, 0, Rational[ 1, 27] $CellContext`c $CellContext`L^(-6) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^6, Rational[ 10, 27] $CellContext`c $CellContext`L^(-6) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^6, Rational[ 1, 27] $CellContext`c $CellContext`L^(-6) $CellContext`n^(-5) ( 1 + $CellContext`n) (1 - 49 $CellContext`n^2 + 48 $CellContext`n^4) Pi^6}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"453600", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "8"], " ", "n"}], ")"}]}]]}], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"90", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "3"]}], ")"}]}]], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"15", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "3"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "11"}], "-", RowBox[{"62", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"3727", " ", SuperscriptBox["n", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"1620", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "7"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[-1, 453600] $CellContext`c $CellContext`L^(-8) $CellContext`n^(-1) ( 1 + $CellContext`n) Pi^8, 0, Rational[-1, 90] $CellContext`c $CellContext`L^(-8) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^8, Rational[-4, 15] $CellContext`c $CellContext`L^(-8) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^8, Rational[-1, 1620] $CellContext`c $CellContext`L^(-8) (-1 + $CellContext`n) \ $CellContext`n^(-7) (1 + $CellContext`n)^2 (-11 - 62 $CellContext`n^2 + 3727 $CellContext`n^4) Pi^8}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 0, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[1, 12] $CellContext`c $CellContext`n^(-1) (1 + $CellContext`n) Log[$CellContext`\[ScriptL]], 0, Rational[-1, 72] $CellContext`c $CellContext`L^(-2) $CellContext`n^(-1) ( 1 + $CellContext`n) Pi^2, 0, SeriesData[$CellContext`q, 0, { Rational[-1, 2160] $CellContext`c $CellContext`L^(-4) $CellContext`n^(-1) ( 1 + $CellContext`n) Pi^4, 0, Rational[-1, 18] $CellContext`c $CellContext`L^(-4) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^4, Rational[-2, 9] $CellContext`c $CellContext`L^(-4) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^4, Rational[-11, 18] $CellContext`c $CellContext`L^(-4) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^4}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, { Rational[-1, 34020] $CellContext`c $CellContext`L^(-6) $CellContext`n^(-1) ( 1 + $CellContext`n) Pi^6, 0, Rational[ 1, 27] $CellContext`c $CellContext`L^(-6) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^6, Rational[ 10, 27] $CellContext`c $CellContext`L^(-6) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^6, Rational[ 1, 27] $CellContext`c $CellContext`L^(-6) $CellContext`n^(-5) ( 1 + $CellContext`n) (1 - 49 $CellContext`n^2 + 48 $CellContext`n^4) Pi^6}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, { Rational[-1, 453600] $CellContext`c $CellContext`L^(-8) $CellContext`n^(-1) ( 1 + $CellContext`n) Pi^8, 0, Rational[-1, 90] $CellContext`c $CellContext`L^(-8) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^8, Rational[-4, 15] $CellContext`c $CellContext`L^(-8) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^8, Rational[-1, 1620] $CellContext`c $CellContext`L^(-8) (-1 + $CellContext`n) \ $CellContext`n^(-7) (1 + $CellContext`n)^2 (-11 - 62 $CellContext`n^2 + 3727 $CellContext`n^4) Pi^8}, 0, 5, 1]}, 0, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.7039551068502264`*^9, 3.703955113794247*^9}, { 3.703956555981813*^9, 3.703956557934515*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SnNLLq", "=", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["q", "2"]}], RowBox[{"3", " ", SuperscriptBox["L", "2"], " ", "n"}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["q", "3"]}], RowBox[{ SuperscriptBox["L", "2"], " ", "n"}]], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["q", "4"]}], RowBox[{ SuperscriptBox["L", "2"], " ", "n"}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 2, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[2, 3] $CellContext`L^(-2) $CellContext`n^(-1) ( 1 + $CellContext`n) Pi^2, $CellContext`L^(-2) $CellContext`n^(-1) (1 + $CellContext`n) Pi^2, 2 $CellContext`L^(-2) $CellContext`n^(-1) (1 + $CellContext`n) Pi^2}, 2, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "2"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "11"}], "+", RowBox[{"9", " ", SuperscriptBox["n", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "4"], " ", SuperscriptBox["n", "3"]}], ")"}]}]]}], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "44"}], "+", RowBox[{"41", " ", SuperscriptBox["n", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"45", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "4"], " ", SuperscriptBox["n", "3"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "51"}], "+", RowBox[{"49", " ", SuperscriptBox["n", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "4"], " ", SuperscriptBox["n", "3"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 2, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[-1, 45] $CellContext`L^(-4) $CellContext`n^(-3) ( 1 + $CellContext`n) (-11 + 9 $CellContext`n^2) Pi^4, Rational[-1, 45] $CellContext`L^(-4) $CellContext`n^(-3) ( 1 + $CellContext`n) (-44 + 41 $CellContext`n^2) Pi^4, Rational[-1, 15] $CellContext`L^(-4) $CellContext`n^(-3) ( 1 + $CellContext`n) (-51 + 49 $CellContext`n^2) Pi^4}, 2, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"31", "-", RowBox[{"46", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"17", " ", SuperscriptBox["n", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", SuperscriptBox["L", "6"], " ", SuperscriptBox["n", "5"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"527", "-", RowBox[{"1013", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"492", " ", SuperscriptBox["n", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "3"]}], RowBox[{"945", " ", SuperscriptBox["L", "6"], " ", SuperscriptBox["n", "5"]}]], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"1255", "-", RowBox[{"2903", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"1654", " ", SuperscriptBox["n", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "4"]}], RowBox[{"945", " ", SuperscriptBox["L", "6"], " ", SuperscriptBox["n", "5"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 2, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[2, 945] $CellContext`L^(-6) $CellContext`n^(-5) ( 1 + $CellContext`n) (31 - 46 $CellContext`n^2 + 17 $CellContext`n^4) Pi^6, Rational[1, 945] $CellContext`L^(-6) $CellContext`n^(-5) ( 1 + $CellContext`n) (527 - 1013 $CellContext`n^2 + 492 $CellContext`n^4) Pi^6, Rational[2, 945] $CellContext`L^(-6) $CellContext`n^(-5) ( 1 + $CellContext`n) (1255 - 2903 $CellContext`n^2 + 1654 $CellContext`n^4) Pi^6}, 2, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "205"}], "+", RowBox[{"415", " ", SuperscriptBox["n", "2"]}], "-", RowBox[{"278", " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"62", " ", SuperscriptBox["n", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"14175", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "7"]}], ")"}]}]]}], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1025"}], "+", RowBox[{"2850", " ", SuperscriptBox["n", "2"]}], "-", RowBox[{"2694", " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"866", " ", SuperscriptBox["n", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"4725", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "7"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "36257"}], "+", RowBox[{"139223", " ", SuperscriptBox["n", "2"]}], "-", RowBox[{"163681", " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"66439", " ", SuperscriptBox["n", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"28350", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "7"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 2, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[-1, 14175] $CellContext`L^(-8) $CellContext`n^(-7) ( 1 + $CellContext`n) (-205 + 415 $CellContext`n^2 - 278 $CellContext`n^4 + 62 $CellContext`n^6) Pi^8, Rational[-1, 4725] $CellContext`L^(-8) $CellContext`n^(-7) ( 1 + $CellContext`n) (-1025 + 2850 $CellContext`n^2 - 2694 $CellContext`n^4 + 866 $CellContext`n^6) Pi^8, Rational[-1, 28350] $CellContext`L^(-8) $CellContext`n^(-7) ( 1 + $CellContext`n) (-36257 + 139223 $CellContext`n^2 - 163681 $CellContext`n^4 + 66439 $CellContext`n^6) Pi^8}, 2, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 2, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, { Rational[2, 3] $CellContext`L^(-2) $CellContext`n^(-1) ( 1 + $CellContext`n) Pi^2, $CellContext`L^(-2) $CellContext`n^(-1) (1 + $CellContext`n) Pi^2, 2 $CellContext`L^(-2) $CellContext`n^(-1) (1 + $CellContext`n) Pi^2}, 2, 5, 1], 0, SeriesData[$CellContext`q, 0, { Rational[-1, 45] $CellContext`L^(-4) $CellContext`n^(-3) ( 1 + $CellContext`n) (-11 + 9 $CellContext`n^2) Pi^4, Rational[-1, 45] $CellContext`L^(-4) $CellContext`n^(-3) ( 1 + $CellContext`n) (-44 + 41 $CellContext`n^2) Pi^4, Rational[-1, 15] $CellContext`L^(-4) $CellContext`n^(-3) ( 1 + $CellContext`n) (-51 + 49 $CellContext`n^2) Pi^4}, 2, 5, 1], 0, SeriesData[$CellContext`q, 0, { Rational[2, 945] $CellContext`L^(-6) $CellContext`n^(-5) ( 1 + $CellContext`n) (31 - 46 $CellContext`n^2 + 17 $CellContext`n^4) Pi^6, Rational[1, 945] $CellContext`L^(-6) $CellContext`n^(-5) ( 1 + $CellContext`n) (527 - 1013 $CellContext`n^2 + 492 $CellContext`n^4) Pi^6, Rational[2, 945] $CellContext`L^(-6) $CellContext`n^(-5) ( 1 + $CellContext`n) (1255 - 2903 $CellContext`n^2 + 1654 $CellContext`n^4) Pi^6}, 2, 5, 1], 0, SeriesData[$CellContext`q, 0, { Rational[-1, 14175] $CellContext`L^(-8) $CellContext`n^(-7) ( 1 + $CellContext`n) (-205 + 415 $CellContext`n^2 - 278 $CellContext`n^4 + 62 $CellContext`n^6) Pi^8, Rational[-1, 4725] $CellContext`L^(-8) $CellContext`n^(-7) ( 1 + $CellContext`n) (-1025 + 2850 $CellContext`n^2 - 2694 $CellContext`n^4 + 866 $CellContext`n^6) Pi^8, Rational[-1, 28350] $CellContext`L^(-8) $CellContext`n^(-7) ( 1 + $CellContext`n) (-36257 + 139223 $CellContext`n^2 - 163681 $CellContext`n^4 + 66439 $CellContext`n^6) Pi^8}, 2, 5, 1]}, 2, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.703955116897028*^9, 3.7039551223823314`*^9}, { 3.703955171543493*^9, 3.703955187624772*^9}, {3.7039565617225666`*^9, 3.703956577006568*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SnNNLLq", "=", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"11", "+", SuperscriptBox["n", "2"]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"45", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L", "4"], " ", SuperscriptBox["n", "3"]}], ")"}]}]]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 4, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[-4, 45] $CellContext`c^(-1) $CellContext`L^(-4) $CellContext`n^(-3) ( 1 + $CellContext`n) (11 + $CellContext`n^2) Pi^4}, 4, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "345"}], "+", RowBox[{"271", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"26", " ", SuperscriptBox["n", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "4"]}], RowBox[{"945", " ", "c", " ", SuperscriptBox["L", "6"], " ", SuperscriptBox["n", "5"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 4, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[ 4, 945] $CellContext`c^(-1) $CellContext`L^(-6) \ $CellContext`n^(-5) (1 + $CellContext`n) (-345 + 271 $CellContext`n^2 + 26 $CellContext`n^4) Pi^6}, 4, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"3398", "-", RowBox[{"3017", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"1141", " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"116", " ", SuperscriptBox["n", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"14175", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "7"]}], ")"}]}]]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 4, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[-8, 14175] $CellContext`c^(-1) $CellContext`L^(-8) \ $CellContext`n^(-7) (1 + $CellContext`n) (3398 - 3017 $CellContext`n^2 + 1141 $CellContext`n^4 + 116 $CellContext`n^6) Pi^8}, 4, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, { Rational[-4, 45] $CellContext`c^(-1) $CellContext`L^(-4) $CellContext`n^(-3) ( 1 + $CellContext`n) (11 + $CellContext`n^2) Pi^4}, 4, 5, 1], 0, SeriesData[$CellContext`q, 0, { Rational[ 4, 945] $CellContext`c^(-1) $CellContext`L^(-6) $CellContext`n^(-5) ( 1 + $CellContext`n) (-345 + 271 $CellContext`n^2 + 26 $CellContext`n^4) Pi^6}, 4, 5, 1], 0, SeriesData[$CellContext`q, 0, { Rational[-8, 14175] $CellContext`c^(-1) $CellContext`L^(-8) $CellContext`n^(-7) ( 1 + $CellContext`n) (3398 - 3017 $CellContext`n^2 + 1141 $CellContext`n^4 + 116 $CellContext`n^6) Pi^8}, 4, 5, 1]}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.703955182440483*^9, 3.703955190249424*^9}, { 3.7039552582887735`*^9, 3.7039552607282867`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SLq", "=", InterpretationBox[ RowBox[{ RowBox[{ FractionBox["1", "6"], " ", "c", " ", RowBox[{"Log", "[", "\[ScriptL]", "]"}]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"c", " ", SuperscriptBox["\[Pi]", "2"]}], RowBox[{"36", " ", SuperscriptBox["L", "2"]}]]}], "+", FractionBox[ RowBox[{"4", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["q", "2"]}], RowBox[{"3", " ", SuperscriptBox["L", "2"]}]], "+", FractionBox[ RowBox[{"2", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["q", "3"]}], SuperscriptBox["L", "2"]], "+", FractionBox[ RowBox[{"4", " ", SuperscriptBox["\[Pi]", "2"], " ", SuperscriptBox["q", "4"]}], SuperscriptBox["L", "2"]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((Rational[-1, 36] $CellContext`c) $CellContext`L^(-2)) Pi^2, 0, (Rational[4, 3] $CellContext`L^(-2)) Pi^2, (2 $CellContext`L^(-2)) Pi^2, (4 $CellContext`L^(-2)) Pi^2}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "2"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"c", " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"1080", " ", SuperscriptBox["L", "4"]}]]}], "+", FractionBox[ RowBox[{"4", " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", SuperscriptBox["L", "4"]}]], "+", FractionBox[ RowBox[{"2", " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "3"]}], RowBox[{"15", " ", SuperscriptBox["L", "4"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((Rational[-1, 1080] $CellContext`c) $CellContext`L^(-4)) Pi^4, 0, (Rational[4, 45] $CellContext`L^(-4)) Pi^4, (Rational[2, 15] $CellContext`L^(-4)) Pi^4, ((( Rational[ 4, 15] (-8 + $CellContext`c))/$CellContext`c) \ $CellContext`L^(-4)) Pi^4}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"c", " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"17010", " ", SuperscriptBox["L", "6"]}]]}], "+", FractionBox[ RowBox[{"8", " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", SuperscriptBox["L", "6"]}]], "+", FractionBox[ RowBox[{"4", " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "3"]}], RowBox[{"315", " ", SuperscriptBox["L", "6"]}]], "+", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "4"]}], RowBox[{"315", " ", "c", " ", SuperscriptBox["L", "6"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((Rational[-1, 17010] $CellContext`c) $CellContext`L^(-6)) Pi^6, 0, (Rational[8, 945] $CellContext`L^(-6)) Pi^6, (Rational[4, 315] $CellContext`L^(-6)) Pi^6, ((( Rational[ 8, 315] (-16 + $CellContext`c))/$CellContext`c) \ $CellContext`L^(-6)) Pi^6}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"c", " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"226800", " ", SuperscriptBox["L", "8"]}]]}], "+", FractionBox[ RowBox[{"4", " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "2"]}], RowBox[{"4725", " ", SuperscriptBox["L", "8"]}]], "+", FractionBox[ RowBox[{"2", " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "3"]}], RowBox[{"1575", " ", SuperscriptBox["L", "8"]}]], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"728", "+", RowBox[{"159", " ", "c"}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"1575", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L", "8"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((Rational[-1, 226800] $CellContext`c) $CellContext`L^(-8)) Pi^8, 0, (Rational[4, 4725] $CellContext`L^(-8)) Pi^8, (Rational[2, 1575] $CellContext`L^(-8)) Pi^8, (((Rational[-4, 1575]/$CellContext`c) (728 + 159 $CellContext`c)) $CellContext`L^(-8)) Pi^8}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 0, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, {(Rational[1, 6] $CellContext`c) Log[$CellContext`\[ScriptL]], 0, SeriesData[$CellContext`q, 0, {((Rational[-1, 36] $CellContext`c) $CellContext`L^(-2)) Pi^2, 0, (Rational[4, 3] $CellContext`L^(-2)) Pi^2, (2 $CellContext`L^(-2)) Pi^2, (4 $CellContext`L^(-2)) Pi^2}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((Rational[-1, 1080] $CellContext`c) $CellContext`L^(-4)) Pi^4, 0, (Rational[4, 45] $CellContext`L^(-4)) Pi^4, (Rational[2, 15] $CellContext`L^(-4)) Pi^4, ((( Rational[ 4, 15] (-8 + $CellContext`c))/$CellContext`c) $CellContext`L^(-4)) Pi^4}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((Rational[-1, 17010] $CellContext`c) $CellContext`L^(-6)) Pi^6, 0, (Rational[8, 945] $CellContext`L^(-6)) Pi^6, (Rational[4, 315] $CellContext`L^(-6)) Pi^6, ((( Rational[ 8, 315] (-16 + $CellContext`c))/$CellContext`c) \ $CellContext`L^(-6)) Pi^6}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((Rational[-1, 226800] $CellContext`c) $CellContext`L^(-8)) Pi^8, 0, (Rational[4, 4725] $CellContext`L^(-8)) Pi^8, (Rational[2, 1575] $CellContext`L^(-8)) Pi^8, (((Rational[-4, 1575]/$CellContext`c) (728 + 159 $CellContext`c)) $CellContext`L^(-8)) Pi^8}, 0, 5, 1]}, 0, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.7039552673682094`*^9, 3.7039552798499975`*^9}}] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Section 3.1 Relative entropy", "Section", CellChangeTimes->{{3.7039542022131257`*^9, 3.703954219345484*^9}, { 3.7039553305656457`*^9, 3.703955332918915*^9}, {3.704042560801203*^9, 3.704042566640339*^9}, 3.704172895928708*^9, {3.7118128992384977`*^9, 3.7118129046913342`*^9}}], Cell[CellGroupData[{ Cell["S(\[Rho]_A(L1,\[Phi]1)||\[Rho]_A(L2,\[Phi]2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9}], Cell[BoxData[ RowBox[{ RowBox[{"SL1\[Phi]1L2\[Phi]2", "=", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["\[ScriptL]", "4"]}], RowBox[{"1080", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["\[ScriptL]", "6"]}], RowBox[{"17010", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"226800", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"352", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]2"}], "+", RowBox[{"512", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"674", "+", RowBox[{"145", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]2", "2"]}], "-", RowBox[{"1351680", " ", "c", " ", RowBox[{"(", RowBox[{"5", "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]2", "3"]}], "+", RowBox[{"184320", " ", RowBox[{"(", RowBox[{"264", "+", RowBox[{"49", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]2", "4"]}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"4", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]2"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]2", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"64", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]1"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]1", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]2"}]}], ")"}], " ", "h\[Phi]2", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"96", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]1"}], "+", RowBox[{"1152", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"82", "+", RowBox[{"15", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]1", "2"]}], "-", RowBox[{"92160", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"3", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]1", "3"]}], "+", RowBox[{"184320", " ", RowBox[{"(", RowBox[{"88", "+", RowBox[{"9", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]1", "4"]}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["\[ScriptL]", "8"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, {((((Rational[ 1, 1080]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)^2) Pi^4, 0, (((((Rational[ 1, 17010] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)^2) (( 2 ($CellContext`c - 24 $CellContext`h\[Phi]2)) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)) Pi^6, 0, (((((Rational[1, 226800] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) ((( 3 $CellContext`c^4) (22 + 5 $CellContext`c) - (( 352 $CellContext`c^3) (22 + 5 $CellContext`c)) $CellContext`h\[Phi]2 + (( 512 $CellContext`c^2) (674 + 145 $CellContext`c)) $CellContext`h\[Phi]2^2 - (( 1351680 $CellContext`c) ( 5 + $CellContext`c)) $CellContext`h\[Phi]2^3 + ( 184320 (264 + 49 $CellContext`c)) $CellContext`h\[Phi]2^4) $CellContext`L1^8 - \ (((((4 (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi]1)) ($CellContext`c - 24 $CellContext`h\[Phi]2)) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi]2 + 1280 $CellContext`h\[Phi]2^2)) $CellContext`L1^6) \ $CellContext`L2^2 - ((((( 64 $CellContext`c) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi]1 + 2880 $CellContext`h\[Phi]1^2)) ($CellContext`c - 22 $CellContext`h\[Phi]2)) $CellContext`h\[Phi]2) \ $CellContext`L1^4) $CellContext`L2^4 + ($CellContext`c^4 (22 + 5 $CellContext`c) - ((96 $CellContext`c^3) (22 + 5 $CellContext`c)) $CellContext`h\[Phi]1 + (( 1152 $CellContext`c^2) (82 + 15 $CellContext`c)) $CellContext`h\[Phi]1^2 - (( 92160 $CellContext`c) (22 + 3 $CellContext`c)) $CellContext`h\[Phi]1^3 + ( 184320 (88 + 9 $CellContext`c)) $CellContext`h\[Phi]1^4) $CellContext`L2^8)) Pi^8}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.704042631409958*^9, 3.704042659643123*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["S(\[Rho]_A(L1,\[Phi])||\[Rho]_A(L2,q))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SL1\[Phi]L2q", "=", RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"1080", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "-", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"15", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}]}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[ 1, 1080] $CellContext`c^(-1) $CellContext`L1^(-4) \ $CellContext`L2^(-4) ( 24 $CellContext`h\[Phi] $CellContext`L2^2 + $CellContext`c \ ($CellContext`L1 - $CellContext`L2) ($CellContext`L1 + $CellContext`L2))^2 Pi^4, 0, Rational[-4, 45] $CellContext`c^(-1) $CellContext`L1^(-2) $CellContext`L2^(-4) ( 24 $CellContext`h\[Phi] $CellContext`L2^2 + $CellContext`c \ ($CellContext`L1 - $CellContext`L2) ($CellContext`L1 + $CellContext`L2)) Pi^4, Rational[-2, 15] $CellContext`c^(-1) $CellContext`L1^(-2) $CellContext`L2^(-4) ( 24 $CellContext`h\[Phi] $CellContext`L2^2 + $CellContext`c \ ($CellContext`L1 - $CellContext`L2) ($CellContext`L1 + $CellContext`L2)) Pi^4, Rational[ 4, 15] $CellContext`c^(-1) $CellContext`L1^(-2) \ $CellContext`L2^(-4) (-(-8 + $CellContext`c) $CellContext`L1^2 + \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2) Pi^4}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", " ", "c", " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"17010", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "-", FractionBox[ RowBox[{"16", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "-", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"315", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "-", FractionBox[ RowBox[{"16", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", "c", " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"315", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[ 1, 17010] $CellContext`c^(-2) $CellContext`L1^(-6) \ $CellContext`L2^(-6) ( 2 $CellContext`c $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2) ( 24 $CellContext`h\[Phi] $CellContext`L2^2 + $CellContext`c \ ($CellContext`L1 - $CellContext`L2) ($CellContext`L1 + $CellContext`L2))^2 Pi^6, 0, Rational[-16, 945] $CellContext`c^(-1) $CellContext`L1^(-2) $CellContext`L2^(-6) \ (24 $CellContext`h\[Phi] $CellContext`L2^2 + $CellContext`c ($CellContext`L1 - \ $CellContext`L2) ($CellContext`L1 + $CellContext`L2)) Pi^6, Rational[-8, 315] $CellContext`c^(-1) $CellContext`L1^(-2) $CellContext`L2^(-6) \ (24 $CellContext`h\[Phi] $CellContext`L2^2 + $CellContext`c ($CellContext`L1 - \ $CellContext`L2) ($CellContext`L1 + $CellContext`L2)) Pi^6, Rational[-16, 315] $CellContext`c^(-2) $CellContext`L1^(-2) $CellContext`L2^(-6) \ ((-16 + $CellContext`c) $CellContext`c $CellContext`L1^2 - (-8 + \ $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2) Pi^6}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{ FractionBox["1", RowBox[{"226800", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"4", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"96", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"1152", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"82", "+", RowBox[{"15", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "-", RowBox[{"92160", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"3", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}], "+", RowBox[{"184320", " ", RowBox[{"(", RowBox[{"88", "+", RowBox[{"9", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "4"]}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}]}], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"31", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"53", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"14175", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "-", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"203", "+", RowBox[{"40", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"379", "+", RowBox[{"80", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"14175", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "-", RowBox[{ FractionBox["1", RowBox[{"14175", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "9184"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1587"}], "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2720"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"159", "+", RowBox[{"110", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "88"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"306", "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[ 1, 226800] $CellContext`c^(-3) (22 + 5 $CellContext`c)^(-1) $CellContext`L1^(-8) $CellContext`L2^(-8) ( 3 $CellContext`c^4 (22 + 5 $CellContext`c) $CellContext`L1^8 - 4 $CellContext`c^3 (22 + 5 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^6 $CellContext`L2^2 + \ ($CellContext`c^4 (22 + 5 $CellContext`c) - 96 $CellContext`c^3 (22 + 5 $CellContext`c) $CellContext`h\[Phi] + 1152 $CellContext`c^2 (82 + 15 $CellContext`c) $CellContext`h\[Phi]^2 - 92160 $CellContext`c (22 + 3 $CellContext`c) $CellContext`h\[Phi]^3 + 184320 (88 + 9 $CellContext`c) $CellContext`h\[Phi]^4) $CellContext`L2^8) Pi^8, 0, Rational[-4, 14175] $CellContext`c^(-1) $CellContext`L1^(-4) \ $CellContext`L2^(-8) ($CellContext`c (31 + 5 $CellContext`c) $CellContext`L1^4 - (53 + 10 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^2 $CellContext`L2^2 + \ ($CellContext`c (22 + 5 $CellContext`c) - 240 (2 + $CellContext`c) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4) Pi^8, Rational[-2, 14175] $CellContext`c^(-1) $CellContext`L1^(-4) \ $CellContext`L2^(-8) ($CellContext`c (203 + 40 $CellContext`c) $CellContext`L1^4 - (379 + 80 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^2 $CellContext`L2^2 + 8 ($CellContext`c (22 + 5 $CellContext`c) - 240 (2 + $CellContext`c) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4) Pi^8, Rational[-4, 14175] $CellContext`c^(-2) (22 + 5 $CellContext`c)^(-1) $CellContext`L1^(-4) $CellContext`L2^(-8) \ ($CellContext`c (22 + 5 $CellContext`c) (-9184 + $CellContext`c (-1587 + 55 $CellContext`c)) $CellContext`L1^4 - (22 + 5 $CellContext`c) (-2720 + $CellContext`c (159 + 110 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^2 $CellContext`L2^2 + \ (-88 + $CellContext`c (306 + 55 $CellContext`c)) ($CellContext`c (22 + 5 $CellContext`c) - 240 (2 + $CellContext`c) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4) Pi^8}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 2, 10, 1], Editable->False]}]}], ";"}]], "Input", CellChangeTimes->{{3.7041154839401503`*^9, 3.7041155058482423`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["S(\[Rho]_A(L1,q)||\[Rho]_A(L2,\[Phi]))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, {3.704116595159308*^9, 3.704116597929334*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SL1qL2\[Phi]", "=", RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{"c", " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"1080", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{"c", " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}]], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{"c", " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "3"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 1080]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^2 - $CellContext`c \ $CellContext`L2^2)^2) Pi^4, 0, ((((Rational[ 4, 45]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-2)) (($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^2 - $CellContext`c \ $CellContext`L2^2)) Pi^4, (((( Rational[ 2, 15]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-2)) (($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^2 - $CellContext`c \ $CellContext`L2^2)) Pi^4, (((( Rational[ 4, 15]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-2)) (($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^2 - (-8 + \ $CellContext`c) $CellContext`L2^2)) Pi^4}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{"c", " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{"c", " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"17010", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], "2"], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], "2"], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "3"]}], RowBox[{"315", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], "2"], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", "c", " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "4"]}], RowBox[{"315", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 17010] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^2 - $CellContext`c \ $CellContext`L2^2)^2) (( 2 ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2 + $CellContext`c \ $CellContext`L2^2)) Pi^6, 0, ((((Rational[ 8, 945] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-4)) (($CellContext`c - 24 $CellContext`h\[Phi])^2 $CellContext`L1^4 - $CellContext`c^2 \ $CellContext`L2^4)) Pi^6, (((( Rational[ 4, 315] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-4)) (($CellContext`c - 24 $CellContext`h\[Phi])^2 $CellContext`L1^4 - $CellContext`c^2 \ $CellContext`L2^4)) Pi^6, (((( Rational[ 8, 315] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-4)) (($CellContext`c - 24 $CellContext`h\[Phi])^2 $CellContext`L1^4 - ((-16 + \ $CellContext`c) $CellContext`c) $CellContext`L2^4)) Pi^6}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{ FractionBox["1", RowBox[{"226800", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"352", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"512", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"674", "+", RowBox[{"145", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "-", RowBox[{"1351680", " ", "c", " ", RowBox[{"(", RowBox[{"5", "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}], "+", RowBox[{"184320", " ", RowBox[{"(", RowBox[{"264", "+", RowBox[{"49", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "4"]}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"4", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"64", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]"}]}], ")"}], " ", "h\[Phi]", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}]}], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"160", " ", "c", " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]"}]}], ")"}], " ", "h\[Phi]", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "2"]}], RowBox[{"4725", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"480", " ", "c", " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]"}]}], ")"}], " ", "h\[Phi]", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "3"]}], RowBox[{"1575", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"3360", " ", "c", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]"}]}], ")"}], " ", "h\[Phi]", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"728", "+", RowBox[{"159", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "4"]}], RowBox[{"1575", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "6"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((((Rational[1, 226800] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) \ (((3 $CellContext`c^4) (22 + 5 $CellContext`c) - ((352 $CellContext`c^3) (22 + 5 $CellContext`c)) $CellContext`h\[Phi] + (( 512 $CellContext`c^2) (674 + 145 $CellContext`c)) $CellContext`h\[Phi]^2 - (( 1351680 $CellContext`c) ( 5 + $CellContext`c)) $CellContext`h\[Phi]^3 + ( 184320 (264 + 49 $CellContext`c)) $CellContext`h\[Phi]^4) $CellContext`L1^8 - \ (((((4 $CellContext`c) (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L1^6) \ $CellContext`L2^2 - (((((64 $CellContext`c^2) (22 + 5 $CellContext`c)) ($CellContext`c - 22 $CellContext`h\[Phi])) $CellContext`h\[Phi]) \ $CellContext`L1^4) $CellContext`L2^4 + ($CellContext`c^4 (22 + 5 $CellContext`c)) $CellContext`L2^8)) Pi^8, 0, ((((Rational[ 4, 4725] $CellContext`c^(-3)) $CellContext`L1^(-8)) \ $CellContext`L2^(-6)) ((($CellContext`c - 24 $CellContext`h\[Phi]) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L1^6 - (((( 160 $CellContext`c) ($CellContext`c - 22 $CellContext`h\[Phi])) $CellContext`h\[Phi]) \ $CellContext`L1^4) $CellContext`L2^2 - $CellContext`c^3 $CellContext`L2^6)) Pi^8, (((( Rational[ 2, 1575] $CellContext`c^(-3)) $CellContext`L1^(-8)) \ $CellContext`L2^(-6)) ((($CellContext`c - 24 $CellContext`h\[Phi]) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L1^6 - (((( 480 $CellContext`c) ($CellContext`c - 22 $CellContext`h\[Phi])) $CellContext`h\[Phi]) \ $CellContext`L1^4) $CellContext`L2^2 - $CellContext`c^3 $CellContext`L2^6)) Pi^8, (((((Rational[4, 1575] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-6)) \ ((((22 + 5 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L1^6 - ((((( 3360 $CellContext`c) (6 + $CellContext`c)) ($CellContext`c - 22 $CellContext`h\[Phi])) $CellContext`h\[Phi]) \ $CellContext`L1^4) $CellContext`L2^2 + (($CellContext`c^2 (22 + 5 $CellContext`c)) (728 + 159 $CellContext`c)) $CellContext`L2^6)) Pi^8}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 2, 10, 1], Editable->False]}]}], ";"}]], "Input", CellChangeTimes->{{3.7041166026352596`*^9, 3.7041166081093407`*^9}, { 3.7041168304221354`*^9, 3.7041168316016054`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["S(\[Rho]_A(L1,q1)||\[Rho]_A(L2,q2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, {3.704116595159308*^9, 3.704116597929334*^9}, {3.7041177049986935`*^9, 3.704117707948104*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SL1q1L2q2", "=", RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"1080", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "-", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"15", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "+", FractionBox[ RowBox[{"4", " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"8", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}], "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "4"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((( Rational[ 1, 1080] $CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) ($CellContext`L1^2 - $CellContext`L2^2)^2) Pi^4, 0, (((((Rational[-4, 45] $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^2 + $CellContext`L1^2 \ $CellContext`q2^2), ((((( Rational[-2, 15] $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^3 + $CellContext`L1^2 \ $CellContext`q2^3), (((( Rational[ 4, 15]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) Pi^4) ( 8 ($CellContext`L2^2 $CellContext`q1^2 - $CellContext`L1^2 \ $CellContext`q2^2)^2 + (($CellContext`c ($CellContext`L1 - $CellContext`L2)) \ ($CellContext`L1 + $CellContext`L2)) ($CellContext`L2^2 $CellContext`q1^4 - \ $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"3", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", SuperscriptBox["L2", "6"]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"17010", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "-", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q1", "2"], "+", RowBox[{"2", " ", SuperscriptBox["q2", "2"]}]}], ")"}]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{"2", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "3"]}], "-", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q1", "3"], "+", RowBox[{"2", " ", SuperscriptBox["q2", "3"]}]}], ")"}]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"315", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "+", FractionBox[ RowBox[{"8", " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{"32", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{"2", " ", SuperscriptBox["L1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}]}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"315", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 17010] $CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ( 2 $CellContext`L1^6 - ( 3 $CellContext`L1^4) $CellContext`L2^2 + $CellContext`L2^6)) Pi^6, 0, (((Rational[-8, 945] $CellContext`L1^(-6)) $CellContext`L2^(-6)) Pi^6) ($CellContext`L2^6 $CellContext`q1^2 + ( 2 $CellContext`L1^6) $CellContext`q2^2 - ($CellContext`L1^4 \ $CellContext`L2^2) ($CellContext`q1^2 + 2 $CellContext`q2^2)), ((( Rational[-4, 315] $CellContext`L1^(-6)) $CellContext`L2^(-6)) Pi^6) ($CellContext`L2^6 $CellContext`q1^3 + ( 2 $CellContext`L1^6) $CellContext`q2^3 - ($CellContext`L1^4 \ $CellContext`L2^2) ($CellContext`q1^3 + 2 $CellContext`q2^3)), (((( Rational[ 8, 315]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) Pi^6) (($CellContext`L2^2 ($CellContext`c $CellContext`L1^4 - (-16 + \ $CellContext`c) $CellContext`L2^4)) $CellContext`q1^4 - ((( 32 $CellContext`L1^4) $CellContext`L2^2) $CellContext`q1^2) \ $CellContext`q2^2 + (( 2 $CellContext`L1^4) ((-(-16 + $CellContext`c)) \ $CellContext`L1^2 + (-8 + $CellContext`c) $CellContext`L2^2)) \ $CellContext`q2^4)}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"4", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "+", SuperscriptBox["L2", "8"]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"226800", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", FractionBox[ RowBox[{"4", " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], "-", SuperscriptBox["L2", "6"]}], ")"}], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "4"], " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"31", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["q2", "2"]}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"14175", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", FractionBox[ RowBox[{"2", " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{"9", " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], "-", SuperscriptBox["L2", "6"]}], ")"}], " ", SuperscriptBox["q1", "3"]}], "-", RowBox[{ SuperscriptBox["L1", "4"], " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"203", "+", RowBox[{"40", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{"8", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["q2", "3"]}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"14175", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"14175", " ", "c", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{"4", " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{"9", " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"728", "+", RowBox[{"159", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{"48", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"53", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{"10", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"9184", "+", RowBox[{ RowBox[{"(", RowBox[{"1587", "-", RowBox[{"55", " ", "c"}]}], ")"}], " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "2720"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"159", "+", RowBox[{"110", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"88", "-", RowBox[{"c", " ", RowBox[{"(", RowBox[{"306", "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((( Rational[ 1, 226800] $CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) ( 3 $CellContext`L1^8 - ( 4 $CellContext`L1^6) $CellContext`L2^2 + $CellContext`L2^8)) Pi^8, 0, (((Rational[4, 14175] $CellContext`L1^(-8)) $CellContext`L2^(-8)) Pi^8) ((( 3 $CellContext`L2^2) ($CellContext`L1^6 - $CellContext`L2^6)) \ $CellContext`q1^2 - ((($CellContext`L1^4 ($CellContext`L1 - $CellContext`L2)) \ ($CellContext`L1 + $CellContext`L2)) ((31 + 5 $CellContext`c) $CellContext`L1^2 - (22 + 5 $CellContext`c) $CellContext`L2^2)) $CellContext`q2^2), ((( Rational[2, 14175] $CellContext`L1^(-8)) $CellContext`L2^(-8)) Pi^8) ((( 9 $CellContext`L2^2) ($CellContext`L1^6 - $CellContext`L2^6)) \ $CellContext`q1^3 - ((($CellContext`L1^4 ($CellContext`L1 - $CellContext`L2)) \ ($CellContext`L1 + $CellContext`L2)) ((203 + 40 $CellContext`c) $CellContext`L1^2 - ( 8 (22 + 5 $CellContext`c)) $CellContext`L2^2)) \ $CellContext`q2^3), (((( Rational[ 4, 14175]/$CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) Pi^8) ((( 9 $CellContext`L2^2) ($CellContext`c $CellContext`L1^6 + (728 + 159 $CellContext`c) $CellContext`L2^6)) $CellContext`q1^4 - \ ((((48 $CellContext`L1^4) $CellContext`L2^2) ((53 + 10 $CellContext`c) $CellContext`L1^2 + ( 10 (22 + 5 $CellContext`c)) $CellContext`L2^2)) $CellContext`q1^2) \ $CellContext`q2^2 + ($CellContext`L1^4 (( 9184 + (1587 - 55 $CellContext`c) $CellContext`c) $CellContext`L1^4 + \ ((-2720 + $CellContext`c (159 + 110 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + \ (88 - $CellContext`c (306 + 55 $CellContext`c)) $CellContext`L2^4)) $CellContext`q2^4)}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 2, 10, 1], Editable->False]}]}], ";"}]], "Input", CellChangeTimes->{{3.7041177096676693`*^9, 3.704117722947776*^9}}] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Section 3.1 Symmetrized relative entropy", "Section", CellChangeTimes->{{3.7039542022131257`*^9, 3.703954219345484*^9}, { 3.7039553305656457`*^9, 3.703955332918915*^9}, {3.704042560801203*^9, 3.704042566640339*^9}, {3.704120014430778*^9, 3.704120020367242*^9}, { 3.7041202566340466`*^9, 3.704120261571334*^9}, {3.7041209819439144`*^9, 3.7041209908712945`*^9}, 3.7041728973297224`*^9, {3.711812916602792*^9, 3.711812920804221*^9}, {3.711812963898788*^9, 3.7118129642735796`*^9}}], Cell[CellGroupData[{ Cell["S(\[Rho]_A(L1,\[Phi]1),\[Rho]_A(L2,\[Phi]2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, 3.704120023776886*^9}], Cell[BoxData[ RowBox[{ RowBox[{"SL1\[Phi]1L2\[Phi]2", "=", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["\[ScriptL]", "4"]}], RowBox[{"540", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["\[ScriptL]", "6"]}], RowBox[{"5670", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"56700", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"22", " ", SuperscriptBox["c", "4"], " ", SuperscriptBox["L1", "8"]}], "+", RowBox[{"5", " ", SuperscriptBox["c", "5"], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"2464", " ", SuperscriptBox["c", "3"], " ", "h\[Phi]2", " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"560", " ", SuperscriptBox["c", "4"], " ", "h\[Phi]2", " ", SuperscriptBox["L1", "8"]}], "+", RowBox[{"109888", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["h\[Phi]2", "2"], " ", SuperscriptBox["L1", "8"]}], "+", RowBox[{"22880", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox["h\[Phi]2", "2"], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"2196480", " ", "c", " ", SuperscriptBox["h\[Phi]2", "3"], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"407040", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["h\[Phi]2", "3"], " ", SuperscriptBox["L1", "8"]}], "+", RowBox[{"16220160", " ", SuperscriptBox["h\[Phi]2", "4"], " ", SuperscriptBox["L1", "8"]}], "+", RowBox[{"2672640", " ", "c", " ", SuperscriptBox["h\[Phi]2", "4"], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]2"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]2", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"16", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]1"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]1", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]2"}]}], ")"}], " ", "h\[Phi]2", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "-", RowBox[{"16", " ", "c", " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]1"}]}], ")"}], " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]2"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]2", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]1"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]1", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], "+", RowBox[{"22", " ", SuperscriptBox["c", "4"], " ", SuperscriptBox["L2", "8"]}], "+", RowBox[{"5", " ", SuperscriptBox["c", "5"], " ", SuperscriptBox["L2", "8"]}], "-", RowBox[{"2464", " ", SuperscriptBox["c", "3"], " ", "h\[Phi]1", " ", SuperscriptBox["L2", "8"]}], "-", RowBox[{"560", " ", SuperscriptBox["c", "4"], " ", "h\[Phi]1", " ", SuperscriptBox["L2", "8"]}], "+", RowBox[{"109888", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["h\[Phi]1", "2"], " ", SuperscriptBox["L2", "8"]}], "+", RowBox[{"22880", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox["h\[Phi]1", "2"], " ", SuperscriptBox["L2", "8"]}], "-", RowBox[{"2196480", " ", "c", " ", SuperscriptBox["h\[Phi]1", "3"], " ", SuperscriptBox["L2", "8"]}], "-", RowBox[{"407040", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["h\[Phi]1", "3"], " ", SuperscriptBox["L2", "8"]}], "+", RowBox[{"16220160", " ", SuperscriptBox["h\[Phi]1", "4"], " ", SuperscriptBox["L2", "8"]}], "+", RowBox[{"2672640", " ", "c", " ", SuperscriptBox["h\[Phi]1", "4"], " ", SuperscriptBox["L2", "8"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["\[ScriptL]", "8"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, {((((Rational[ 1, 540]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)^2) Pi^4, 0, (((((Rational[ 1, 5670] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)^2) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)) Pi^6, 0, (((((Rational[1, 56700] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) (( 22 $CellContext`c^4) $CellContext`L1^8 + ( 5 $CellContext`c^5) $CellContext`L1^8 - (( 2464 $CellContext`c^3) $CellContext`h\[Phi]2) $CellContext`L1^8 - (( 560 $CellContext`c^4) $CellContext`h\[Phi]2) $CellContext`L1^8 + (( 109888 $CellContext`c^2) $CellContext`h\[Phi]2^2) \ $CellContext`L1^8 + (( 22880 $CellContext`c^3) $CellContext`h\[Phi]2^2) $CellContext`L1^8 - \ ((2196480 $CellContext`c) $CellContext`h\[Phi]2^3) $CellContext`L1^8 - (( 407040 $CellContext`c^2) $CellContext`h\[Phi]2^3) $CellContext`L1^8 + \ (16220160 $CellContext`h\[Phi]2^4) $CellContext`L1^8 + (( 2672640 $CellContext`c) $CellContext`h\[Phi]2^4) $CellContext`L1^8 - \ (((((22 + 5 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi]1)) ($CellContext`c - 24 $CellContext`h\[Phi]2)) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi]2 + 1280 $CellContext`h\[Phi]2^2)) $CellContext`L1^6) \ $CellContext`L2^2 - ((((( 16 $CellContext`c) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi]1 + 2880 $CellContext`h\[Phi]1^2)) ($CellContext`c - 22 $CellContext`h\[Phi]2)) $CellContext`h\[Phi]2) \ $CellContext`L1^4) $CellContext`L2^4 - ((((( 16 $CellContext`c) ($CellContext`c - 22 $CellContext`h\[Phi]1)) $CellContext`h\[Phi]1) \ ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi]2 + 2880 $CellContext`h\[Phi]2^2)) $CellContext`L1^4) \ $CellContext`L2^4 - (((((22 + 5 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi]1)) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi]1 + 1280 $CellContext`h\[Phi]1^2)) ($CellContext`c - 24 $CellContext`h\[Phi]2)) $CellContext`L1^2) $CellContext`L2^6 + ( 22 $CellContext`c^4) $CellContext`L2^8 + ( 5 $CellContext`c^5) $CellContext`L2^8 - (( 2464 $CellContext`c^3) $CellContext`h\[Phi]1) $CellContext`L2^8 - (( 560 $CellContext`c^4) $CellContext`h\[Phi]1) $CellContext`L2^8 + (( 109888 $CellContext`c^2) $CellContext`h\[Phi]1^2) \ $CellContext`L2^8 + (( 22880 $CellContext`c^3) $CellContext`h\[Phi]1^2) $CellContext`L2^8 - \ ((2196480 $CellContext`c) $CellContext`h\[Phi]1^3) $CellContext`L2^8 - (( 407040 $CellContext`c^2) $CellContext`h\[Phi]1^3) $CellContext`L2^8 + \ (16220160 $CellContext`h\[Phi]1^4) $CellContext`L2^8 + (( 2672640 $CellContext`c) $CellContext`h\[Phi]1^4) \ $CellContext`L2^8)) Pi^8}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.704042631409958*^9, 3.704042659643123*^9}, 3.7041200337358904`*^9, {3.7041210298822193`*^9, 3.7041210316822205`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["S(\[Rho]_A(L1,\[Phi]),\[Rho]_A(L2,q))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, 3.7041200258581767`*^9}], Cell[BoxData[ RowBox[{ RowBox[{"SL1\[Phi]L2q", "=", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"540", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "-", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"15", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "+", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}]}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 540]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^4, 0, (((( Rational[-8, 45]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^4, (((( Rational[-4, 15]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^4, (((( Rational[ 8, 15]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-(-8 + $CellContext`c)) $CellContext`L1^2 + \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"5670", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "-", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", "c", " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", "c", " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"315", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "-", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", "c", " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], "2"], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"315", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 5670] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`c $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^6, 0, ((((( Rational[-8, 945] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((3 $CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, ((((( Rational[-4, 315] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((3 $CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, (((( Rational[-8, 315] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((( 3 (-16 + $CellContext`c)) $CellContext`c) $CellContext`L1^4 - \ (((2 (-8 + $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 - \ ($CellContext`c - 24 $CellContext`h\[Phi])^2 $CellContext`L2^4)) Pi^6}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{ FractionBox["1", RowBox[{"56700", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{ SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"16", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]"}]}], ")"}], " ", "h\[Phi]", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "-", RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"112", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"32", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"3434", "+", RowBox[{"715", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "-", RowBox[{"7680", " ", "c", " ", RowBox[{"(", RowBox[{"286", "+", RowBox[{"53", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}], "+", RowBox[{"92160", " ", RowBox[{"(", RowBox[{"176", "+", RowBox[{"29", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "4"]}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}]}], "-", RowBox[{ FractionBox["1", RowBox[{"14175", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"34", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"53", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", SuperscriptBox["c", "2"], " ", "h\[Phi]"}], "+", RowBox[{"960", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "11"}], "+", RowBox[{"3", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "-", RowBox[{"3", " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "2"]}]}], "-", RowBox[{ FractionBox["1", RowBox[{"14175", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"4", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"53", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"379", "+", RowBox[{"80", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"8", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "+", RowBox[{"60", " ", RowBox[{"(", RowBox[{"1", "-", RowBox[{"4", " ", "c"}]}], ")"}], " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"360", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "33"}], "+", RowBox[{"8", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "-", RowBox[{"9", " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "3"]}]}], "+", RowBox[{ FractionBox["1", RowBox[{"14175", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "9184"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1587"}], "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2720"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"159", "+", RowBox[{"110", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "88"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"306", "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}]}], "+", RowBox[{"9", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"728", "+", RowBox[{"159", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"3360", " ", "c", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]"}]}], ")"}], " ", "h\[Phi]", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], "-", RowBox[{"80", " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"1280", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((((Rational[1, 56700] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) \ (($CellContext`c^4 (22 + 5 $CellContext`c)) $CellContext`L1^8 - ((($CellContext`c^3 (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^6) $CellContext`L2^2 - \ (((((16 $CellContext`c^2) (22 + 5 $CellContext`c)) ($CellContext`c - 22 $CellContext`h\[Phi])) $CellContext`h\[Phi]) \ $CellContext`L1^4) $CellContext`L2^4 - (((($CellContext`c (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^6 + ($CellContext`c^4 (22 + 5 $CellContext`c) - (( 112 $CellContext`c^3) (22 + 5 $CellContext`c)) $CellContext`h\[Phi] + (( 32 $CellContext`c^2) (3434 + 715 $CellContext`c)) $CellContext`h\[Phi]^2 - (( 7680 $CellContext`c) (286 + 53 $CellContext`c)) $CellContext`h\[Phi]^3 + ( 92160 (176 + 29 $CellContext`c)) $CellContext`h\[Phi]^4) \ $CellContext`L2^8)) Pi^8, 0, ((((Rational[-4, 14175] $CellContext`c^(-3)) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c^3 (34 + 5 $CellContext`c)) $CellContext`L1^6 - ((($CellContext`c^2 (53 + 10 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ (($CellContext`c ($CellContext`c^2 (22 + 5 $CellContext`c) - ( 240 $CellContext`c^2) $CellContext`h\[Phi] + ( 960 (-11 + 3 $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^4 - (( 3 ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L2^6)) Pi^8, (((( Rational[-2, 14175] $CellContext`c^(-3)) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (((4 $CellContext`c^3) (53 + 10 $CellContext`c)) $CellContext`L1^6 - ((($CellContext`c^2 ( 379 + 80 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ (((8 $CellContext`c) ($CellContext`c^2 (22 + 5 $CellContext`c) + (( 60 (1 - 4 $CellContext`c)) $CellContext`c) $CellContext`h\[Phi] + \ (360 (-33 + 8 $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^4 - (( 9 ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L2^6)) Pi^8, (((((Rational[4, 14175] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-6)) $CellContext`L2^(-8)) \ (((-$CellContext`c) $CellContext`L1^2) ((($CellContext`c (22 + 5 $CellContext`c)) (-9184 + $CellContext`c (-1587 + 55 $CellContext`c))) $CellContext`L1^4 - ((((22 + 5 $CellContext`c) (-2720 + $CellContext`c (159 + 110 $CellContext`c))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) \ $CellContext`L2^2 + ((-88 + $CellContext`c (306 + 55 $CellContext`c)) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2)) $CellContext`L2^4) + 9 ((($CellContext`c^2 (22 + 5 $CellContext`c)) (728 + 159 $CellContext`c)) $CellContext`L1^6 - ((((( 3360 $CellContext`c) (6 + $CellContext`c)) ($CellContext`c - 22 $CellContext`h\[Phi])) $CellContext`h\[Phi]) \ $CellContext`L1^2) $CellContext`L2^4 + (((22 + 5 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L2^6))) Pi^8}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, {((((Rational[ 1, 540]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^4, 0, (((( Rational[-8, 45]/$CellContext`c) $CellContext`L1^(-2)) $CellContext`L2^(-4)) \ ((24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^4, (((( Rational[-4, 15]/$CellContext`c) $CellContext`L1^(-2)) $CellContext`L2^(-4)) \ ((24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^4, (((( Rational[ 8, 15]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-(-8 + $CellContext`c)) $CellContext`L1^2 + \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 5670] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`c $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^6, 0, ((((( Rational[-8, 945] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((3 $CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, ((((( Rational[-4, 315] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((3 $CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, (((( Rational[-8, 315] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((( 3 (-16 + $CellContext`c)) $CellContext`c) $CellContext`L1^4 - ((( 2 (-8 + $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 - \ ($CellContext`c - 24 $CellContext`h\[Phi])^2 $CellContext`L2^4)) Pi^6}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {(((((Rational[1, 56700] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) \ (($CellContext`c^4 (22 + 5 $CellContext`c)) $CellContext`L1^8 - ((($CellContext`c^3 (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^6) $CellContext`L2^2 - \ (((((16 $CellContext`c^2) (22 + 5 $CellContext`c)) ($CellContext`c - 22 $CellContext`h\[Phi])) $CellContext`h\[Phi]) \ $CellContext`L1^4) $CellContext`L2^4 - (((($CellContext`c (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^6 + ($CellContext`c^4 (22 + 5 $CellContext`c) - (( 112 $CellContext`c^3) (22 + 5 $CellContext`c)) $CellContext`h\[Phi] + (( 32 $CellContext`c^2) (3434 + 715 $CellContext`c)) $CellContext`h\[Phi]^2 - (( 7680 $CellContext`c) (286 + 53 $CellContext`c)) $CellContext`h\[Phi]^3 + ( 92160 (176 + 29 $CellContext`c)) $CellContext`h\[Phi]^4) $CellContext`L2^8)) Pi^8, 0, (((( Rational[-4, 14175] $CellContext`c^(-3)) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c^3 (34 + 5 $CellContext`c)) $CellContext`L1^6 - ((($CellContext`c^2 (53 + 10 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ (($CellContext`c ($CellContext`c^2 (22 + 5 $CellContext`c) - ( 240 $CellContext`c^2) $CellContext`h\[Phi] + ( 960 (-11 + 3 $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^4 - (( 3 ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L2^6)) Pi^8, (((( Rational[-2, 14175] $CellContext`c^(-3)) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (((4 $CellContext`c^3) (53 + 10 $CellContext`c)) $CellContext`L1^6 - ((($CellContext`c^2 (379 + 80 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ (((8 $CellContext`c) ($CellContext`c^2 (22 + 5 $CellContext`c) + (( 60 (1 - 4 $CellContext`c)) $CellContext`c) $CellContext`h\[Phi] + ( 360 (-33 + 8 $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^4 - (( 9 ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L2^6)) Pi^8, (((((Rational[4, 14175] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-6)) $CellContext`L2^(-8)) \ (((-$CellContext`c) $CellContext`L1^2) ((($CellContext`c (22 + 5 $CellContext`c)) (-9184 + $CellContext`c (-1587 + 55 $CellContext`c))) $CellContext`L1^4 - ((((22 + 5 $CellContext`c) (-2720 + $CellContext`c (159 + 110 $CellContext`c))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ ((-88 + $CellContext`c (306 + 55 $CellContext`c)) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2)) $CellContext`L2^4) + 9 ((($CellContext`c^2 (22 + 5 $CellContext`c)) (728 + 159 $CellContext`c)) $CellContext`L1^6 - ((((( 3360 $CellContext`c) (6 + $CellContext`c)) ($CellContext`c - 22 $CellContext`h\[Phi])) $CellContext`h\[Phi]) \ $CellContext`L1^2) $CellContext`L2^4 + (((22 + 5 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 - ( 80 $CellContext`c) $CellContext`h\[Phi] + 1280 $CellContext`h\[Phi]^2)) $CellContext`L2^6))) Pi^8}, 0, 5, 1]}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.7041154839401503`*^9, 3.7041155058482423`*^9}, 3.7041200391757126`*^9, {3.704121477809372*^9, 3.704121478941149*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["S(\[Rho]_A(L1,q1),\[Rho]_A(L2,q2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, {3.704116595159308*^9, 3.704116597929334*^9}, {3.7041177049986935`*^9, 3.704117707948104*^9}, 3.704120028560308*^9}], Cell[BoxData[ RowBox[{ RowBox[{"SL1q1L2q2", "=", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"540", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "-", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"15", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "+", FractionBox[ RowBox[{"8", " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"8", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}], "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "4"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[ 1, 540] $CellContext`c $CellContext`L1^(-4) $CellContext`L2^(-4) \ ($CellContext`L1^2 - $CellContext`L2^2)^2 Pi^4, 0, Rational[-8, 45] $CellContext`L1^(-4) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-4) ($CellContext`L1 + $CellContext`L2) Pi^4 (-$CellContext`L2^2 $CellContext`q1^2 + $CellContext`L1^2 \ $CellContext`q2^2), Rational[-4, 15] $CellContext`L1^(-4) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-4) ($CellContext`L1 + $CellContext`L2) Pi^4 (-$CellContext`L2^2 $CellContext`q1^3 + $CellContext`L1^2 \ $CellContext`q2^3), Rational[ 8, 15] $CellContext`c^(-1) $CellContext`L1^(-4) \ $CellContext`L2^(-4) Pi^4 (8 ($CellContext`L2^2 $CellContext`q1^2 - $CellContext`L1^2 \ $CellContext`q2^2)^2 + $CellContext`c ($CellContext`L1 - $CellContext`L2) \ ($CellContext`L1 + $CellContext`L2) ($CellContext`L2^2 $CellContext`q1^4 - \ $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "+", SuperscriptBox["L2", "2"]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"5670", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "-", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", SuperscriptBox["L2", "4"], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{"3", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["q1", "2"]}], "+", SuperscriptBox["q2", "2"]}], ")"}]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "-", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", SuperscriptBox["L2", "4"], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{"3", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["q2", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["q1", "3"]}], "+", SuperscriptBox["q2", "3"]}], ")"}]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"315", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "+", FractionBox[ RowBox[{"8", " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"3", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{"32", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "+", SuperscriptBox["L2", "2"]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"315", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[ 1, 5670] $CellContext`c $CellContext`L1^(-6) $CellContext`L2^(-6) \ ($CellContext`L1^2 - $CellContext`L2^2)^2 ($CellContext`L1^2 + \ $CellContext`L2^2) Pi^6, 0, Rational[-8, 945] $CellContext`L1^(-6) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-6) ($CellContext`L1 + $CellContext`L2) Pi^6 ((-3) $CellContext`L2^4 $CellContext`q1^2 + 3 $CellContext`L1^4 $CellContext`q2^2 + $CellContext`L1^2 \ $CellContext`L2^2 (-$CellContext`q1^2 + $CellContext`q2^2)), Rational[-4, 315] $CellContext`L1^(-6) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-6) ($CellContext`L1 + $CellContext`L2) Pi^6 ((-3) $CellContext`L2^4 $CellContext`q1^3 + 3 $CellContext`L1^4 $CellContext`q2^3 + $CellContext`L1^2 \ $CellContext`L2^2 (-$CellContext`q1^3 + $CellContext`q2^3)), Rational[ 8, 315] $CellContext`c^(-1) $CellContext`L1^(-6) \ $CellContext`L2^(-6) Pi^6 ($CellContext`L2^2 ($CellContext`c $CellContext`L1^4 + 2 (-8 + $CellContext`c) $CellContext`L1^2 $CellContext`L2^2 - 3 (-16 + $CellContext`c) $CellContext`L2^4) $CellContext`q1^4 - 32 $CellContext`L1^2 $CellContext`L2^2 ($CellContext`L1^2 + \ $CellContext`L2^2) $CellContext`q1^2 $CellContext`q2^2 + $CellContext`L1^2 \ ((-3) (-16 + $CellContext`c) $CellContext`L1^4 + 2 (-8 + $CellContext`c) $CellContext`L1^2 $CellContext`L2^2 + \ $CellContext`c $CellContext`L2^4) $CellContext`q2^4)}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "8"], "-", RowBox[{ SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], "+", SuperscriptBox["L2", "8"]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"56700", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"34", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"34", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"19", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{"3", " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"19", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"14175", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", RowBox[{"(", RowBox[{"53", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "3"]}], "-", RowBox[{"4", " ", RowBox[{"(", RowBox[{"53", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "3"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"167", "+", RowBox[{"40", " ", "c"}]}], ")"}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{"9", " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"9", " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"167", "+", RowBox[{"40", " ", "c"}]}], ")"}], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"14175", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"14175", " ", "c", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{"4", " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"9", " ", "c", " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"88", "-", RowBox[{"c", " ", RowBox[{"(", RowBox[{"306", "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "2720"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"159", "+", RowBox[{"110", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"15736", "+", RowBox[{ RowBox[{"(", RowBox[{"3018", "-", RowBox[{"55", " ", "c"}]}], ")"}], " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{"48", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"53", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"20", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"53", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"15736", "+", RowBox[{ RowBox[{"(", RowBox[{"3018", "-", RowBox[{"55", " ", "c"}]}], ")"}], " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "2720"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"159", "+", RowBox[{"110", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"88", "-", RowBox[{"c", " ", RowBox[{"(", RowBox[{"306", "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{"9", " ", "c", " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, { Rational[ 1, 56700] $CellContext`c $CellContext`L1^(-8) $CellContext`L2^(-8) \ ($CellContext`L1^8 - $CellContext`L1^6 $CellContext`L2^2 - $CellContext`L1^2 \ $CellContext`L2^6 + $CellContext`L2^8) Pi^8, 0, Rational[ 4, 14175] $CellContext`L1^(-8) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-8) ($CellContext`L1 + $CellContext`L2) Pi^8 ((34 + 5 $CellContext`c) $CellContext`L2^6 $CellContext`q1^2 - (34 + 5 $CellContext`c) $CellContext`L1^6 $CellContext`q2^2 - \ $CellContext`L1^2 $CellContext`L2^4 ((19 + 5 $CellContext`c) $CellContext`q1^2 + 3 $CellContext`q2^2) + $CellContext`L1^4 $CellContext`L2^2 ( 3 $CellContext`q1^2 + (19 + 5 $CellContext`c) $CellContext`q2^2)), Rational[ 2, 14175] $CellContext`L1^(-8) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-8) ($CellContext`L1 + $CellContext`L2) Pi^8 (4 (53 + 10 $CellContext`c) $CellContext`L2^6 $CellContext`q1^3 - 4 (53 + 10 $CellContext`c) $CellContext`L1^6 $CellContext`q2^3 - \ $CellContext`L1^2 $CellContext`L2^4 ((167 + 40 $CellContext`c) $CellContext`q1^3 + 9 $CellContext`q2^3) + $CellContext`L1^4 $CellContext`L2^2 ( 9 $CellContext`q1^3 + (167 + 40 $CellContext`c) $CellContext`q2^3)), Rational[ 4, 14175] $CellContext`c^(-1) $CellContext`L1^(-8) \ $CellContext`L2^(-8) Pi^8 ($CellContext`L2^2 ( 9 $CellContext`c $CellContext`L1^6 + ( 88 - $CellContext`c (306 + 55 $CellContext`c)) $CellContext`L1^4 $CellContext`L2^2 + \ (-2720 + $CellContext`c (159 + 110 $CellContext`c)) $CellContext`L1^2 $CellContext`L2^4 + ( 15736 + (3018 - 55 $CellContext`c) $CellContext`c) $CellContext`L2^6) \ $CellContext`q1^4 - 48 $CellContext`L1^2 $CellContext`L2^2 ((53 + 10 $CellContext`c) $CellContext`L1^4 + 20 (22 + 5 $CellContext`c) $CellContext`L1^2 $CellContext`L2^2 + ( 53 + 10 $CellContext`c) $CellContext`L2^4) $CellContext`q1^2 \ $CellContext`q2^2 + $CellContext`L1^2 (( 15736 + (3018 - 55 $CellContext`c) $CellContext`c) $CellContext`L1^6 + \ (-2720 + $CellContext`c (159 + 110 $CellContext`c)) $CellContext`L1^4 $CellContext`L2^2 + ( 88 - $CellContext`c (306 + 55 $CellContext`c)) $CellContext`L1^2 $CellContext`L2^4 + 9 $CellContext`c $CellContext`L2^6) $CellContext`q2^4)}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, { Rational[ 1, 540] $CellContext`c $CellContext`L1^(-4) $CellContext`L2^(-4) \ ($CellContext`L1^2 - $CellContext`L2^2)^2 Pi^4, 0, Rational[-8, 45] $CellContext`L1^(-4) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-4) ($CellContext`L1 + $CellContext`L2) Pi^4 (-$CellContext`L2^2 $CellContext`q1^2 + $CellContext`L1^2 \ $CellContext`q2^2), Rational[-4, 15] $CellContext`L1^(-4) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-4) ($CellContext`L1 + $CellContext`L2) Pi^4 (-$CellContext`L2^2 $CellContext`q1^3 + $CellContext`L1^2 \ $CellContext`q2^3), Rational[ 8, 15] $CellContext`c^(-1) $CellContext`L1^(-4) $CellContext`L2^(-4) Pi^4 (8 ($CellContext`L2^2 $CellContext`q1^2 - $CellContext`L1^2 \ $CellContext`q2^2)^2 + $CellContext`c ($CellContext`L1 - $CellContext`L2) \ ($CellContext`L1 + $CellContext`L2) ($CellContext`L2^2 $CellContext`q1^4 - \ $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, { Rational[ 1, 5670] $CellContext`c $CellContext`L1^(-6) $CellContext`L2^(-6) \ ($CellContext`L1^2 - $CellContext`L2^2)^2 ($CellContext`L1^2 + \ $CellContext`L2^2) Pi^6, 0, Rational[-8, 945] $CellContext`L1^(-6) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-6) ($CellContext`L1 + $CellContext`L2) Pi^6 ((-3) $CellContext`L2^4 $CellContext`q1^2 + 3 $CellContext`L1^4 $CellContext`q2^2 + $CellContext`L1^2 \ $CellContext`L2^2 (-$CellContext`q1^2 + $CellContext`q2^2)), Rational[-4, 315] $CellContext`L1^(-6) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-6) ($CellContext`L1 + $CellContext`L2) Pi^6 ((-3) $CellContext`L2^4 $CellContext`q1^3 + 3 $CellContext`L1^4 $CellContext`q2^3 + $CellContext`L1^2 \ $CellContext`L2^2 (-$CellContext`q1^3 + $CellContext`q2^3)), Rational[ 8, 315] $CellContext`c^(-1) $CellContext`L1^(-6) $CellContext`L2^(-6) Pi^6 ($CellContext`L2^2 ($CellContext`c $CellContext`L1^4 + 2 (-8 + $CellContext`c) $CellContext`L1^2 $CellContext`L2^2 - 3 (-16 + $CellContext`c) $CellContext`L2^4) $CellContext`q1^4 - 32 $CellContext`L1^2 $CellContext`L2^2 ($CellContext`L1^2 + \ $CellContext`L2^2) $CellContext`q1^2 $CellContext`q2^2 + $CellContext`L1^2 \ ((-3) (-16 + $CellContext`c) $CellContext`L1^4 + 2 (-8 + $CellContext`c) $CellContext`L1^2 $CellContext`L2^2 + \ $CellContext`c $CellContext`L2^4) $CellContext`q2^4)}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, { Rational[ 1, 56700] $CellContext`c $CellContext`L1^(-8) $CellContext`L2^(-8) \ ($CellContext`L1^8 - $CellContext`L1^6 $CellContext`L2^2 - $CellContext`L1^2 \ $CellContext`L2^6 + $CellContext`L2^8) Pi^8, 0, Rational[ 4, 14175] $CellContext`L1^(-8) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-8) ($CellContext`L1 + $CellContext`L2) Pi^8 ((34 + 5 $CellContext`c) $CellContext`L2^6 $CellContext`q1^2 - ( 34 + 5 $CellContext`c) $CellContext`L1^6 $CellContext`q2^2 - \ $CellContext`L1^2 $CellContext`L2^4 ((19 + 5 $CellContext`c) $CellContext`q1^2 + 3 $CellContext`q2^2) + $CellContext`L1^4 $CellContext`L2^2 ( 3 $CellContext`q1^2 + (19 + 5 $CellContext`c) $CellContext`q2^2)), Rational[ 2, 14175] $CellContext`L1^(-8) ($CellContext`L1 - $CellContext`L2) \ $CellContext`L2^(-8) ($CellContext`L1 + $CellContext`L2) Pi^8 (4 (53 + 10 $CellContext`c) $CellContext`L2^6 $CellContext`q1^3 - 4 (53 + 10 $CellContext`c) $CellContext`L1^6 $CellContext`q2^3 - \ $CellContext`L1^2 $CellContext`L2^4 ((167 + 40 $CellContext`c) $CellContext`q1^3 + 9 $CellContext`q2^3) + $CellContext`L1^4 $CellContext`L2^2 ( 9 $CellContext`q1^3 + (167 + 40 $CellContext`c) $CellContext`q2^3)), Rational[ 4, 14175] $CellContext`c^(-1) $CellContext`L1^(-8) \ $CellContext`L2^(-8) Pi^8 ($CellContext`L2^2 ( 9 $CellContext`c $CellContext`L1^6 + ( 88 - $CellContext`c (306 + 55 $CellContext`c)) $CellContext`L1^4 $CellContext`L2^2 + \ (-2720 + $CellContext`c (159 + 110 $CellContext`c)) $CellContext`L1^2 $CellContext`L2^4 + ( 15736 + (3018 - 55 $CellContext`c) $CellContext`c) $CellContext`L2^6) \ $CellContext`q1^4 - 48 $CellContext`L1^2 $CellContext`L2^2 ((53 + 10 $CellContext`c) $CellContext`L1^4 + 20 (22 + 5 $CellContext`c) $CellContext`L1^2 $CellContext`L2^2 + ( 53 + 10 $CellContext`c) $CellContext`L2^4) $CellContext`q1^2 \ $CellContext`q2^2 + $CellContext`L1^2 (( 15736 + (3018 - 55 $CellContext`c) $CellContext`c) $CellContext`L1^6 + (-2720 + \ $CellContext`c (159 + 110 $CellContext`c)) $CellContext`L1^4 $CellContext`L2^2 + ( 88 - $CellContext`c (306 + 55 $CellContext`c)) $CellContext`L1^2 $CellContext`L2^4 + 9 $CellContext`c $CellContext`L2^6) $CellContext`q2^4)}, 0, 5, 1]}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.7041177096676693`*^9, 3.704117722947776*^9}, 3.7041200520732484`*^9, {3.7041226550152373`*^9, 3.7041226564326105`*^9}}] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Section 3.1 2nd symmetrized relative entropy", "Section", CellChangeTimes->{{3.7039542022131257`*^9, 3.703954219345484*^9}, { 3.7039553305656457`*^9, 3.703955332918915*^9}, {3.704042560801203*^9, 3.704042566640339*^9}, {3.704120014430778*^9, 3.704120020367242*^9}, { 3.704120063669981*^9, 3.7041200710617695`*^9}, 3.7041202585198755`*^9, 3.7041728989841805`*^9, {3.711812939626026*^9, 3.711812967570948*^9}}], Cell[CellGroupData[{ Cell["S_2(\[Rho]_A(L1,\[Phi]1),\[Rho]_A(L2,\[Phi]2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, 3.704120023776886*^9, {3.704120076714172*^9, 3.704120078900853*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"S2L1\[Phi]1L2\[Phi]2", "=", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["\[ScriptL]", "4"]}], RowBox[{"4608", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"11", " ", "c", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], "-", SuperscriptBox["L2", "4"]}], ")"}]}], "+", RowBox[{"240", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "h\[Phi]2"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"h\[Phi]1", " ", SuperscriptBox["L2", "4"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["\[ScriptL]", "6"]}], RowBox[{"552960", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"1238630400", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2153", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"95520", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]2"}], "+", RowBox[{"967680", " ", "c", " ", RowBox[{"(", RowBox[{"24", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]2", "2"]}], "+", RowBox[{"19353600", " ", "c", " ", SuperscriptBox["h\[Phi]2", "3"]}], "-", RowBox[{"212889600", " ", SuperscriptBox["h\[Phi]2", "4"]}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"20", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"73", " ", "c"}], "-", RowBox[{"1512", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"126", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"11", " ", "c"}], "-", RowBox[{"240", " ", "h\[Phi]1"}]}], ")"}]}], "-", RowBox[{"240", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"80", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", "h\[Phi]1"}], "-", RowBox[{"640", " ", SuperscriptBox["h\[Phi]1", "2"]}]}], ")"}], " ", "h\[Phi]2"}], "+", RowBox[{"153600", " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"22", " ", "h\[Phi]1"}]}], ")"}], " ", "h\[Phi]1", " ", SuperscriptBox["h\[Phi]2", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "-", RowBox[{"20", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"73", " ", "c"}], "-", RowBox[{"1512", " ", "h\[Phi]1"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2153", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"95520", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]1"}], "+", RowBox[{"967680", " ", "c", " ", RowBox[{"(", RowBox[{"24", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]1", "2"]}], "+", RowBox[{"19353600", " ", "c", " ", SuperscriptBox["h\[Phi]1", "3"]}], "-", RowBox[{"212889600", " ", SuperscriptBox["h\[Phi]1", "4"]}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["\[ScriptL]", "8"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, {((((Rational[ 1, 4608]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)^2) Pi^4, 0, (((((Rational[ 1, 552960]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)) (( 11 $CellContext`c) ($CellContext`L1^4 - $CellContext`L2^4) + 240 ((-$CellContext`h\[Phi]2) $CellContext`L1^4 + \ $CellContext`h\[Phi]1 $CellContext`L2^4))) Pi^6, 0, (((((Rational[1, 1238630400] $CellContext`c^(-2))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) ((( 2153 $CellContext`c^3) (22 + 5 $CellContext`c) - (( 95520 $CellContext`c^2) (22 + 5 $CellContext`c)) $CellContext`h\[Phi]2 + (( 967680 $CellContext`c) (24 + 5 $CellContext`c)) $CellContext`h\[Phi]2^2 + ( 19353600 $CellContext`c) $CellContext`h\[Phi]2^3 - 212889600 $CellContext`h\[Phi]2^4) $CellContext`L1^8 - ((((( 20 $CellContext`c) (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi]1)) (73 $CellContext`c - 1512 $CellContext`h\[Phi]2)) $CellContext`L1^6) $CellContext`L2^2 - \ ((126 (($CellContext`c^2 (22 + 5 $CellContext`c)) (11 $CellContext`c - 240 $CellContext`h\[Phi]1) - (( 240 $CellContext`c) ($CellContext`c (22 + 5 $CellContext`c) - ( 80 (6 + $CellContext`c)) $CellContext`h\[Phi]1 - 640 $CellContext`h\[Phi]1^2)) $CellContext`h\[Phi]2 + (( 153600 ($CellContext`c - 22 $CellContext`h\[Phi]1)) $CellContext`h\[Phi]1) \ $CellContext`h\[Phi]2^2)) $CellContext`L1^4) $CellContext`L2^4 - ((((( 20 $CellContext`c) (22 + 5 $CellContext`c)) (73 $CellContext`c - 1512 $CellContext`h\[Phi]1)) ($CellContext`c - 24 $CellContext`h\[Phi]2)) $CellContext`L1^2) $CellContext`L2^6 + \ ((2153 $CellContext`c^3) (22 + 5 $CellContext`c) - ((95520 $CellContext`c^2) ( 22 + 5 $CellContext`c)) $CellContext`h\[Phi]1 + (( 967680 $CellContext`c) (24 + 5 $CellContext`c)) $CellContext`h\[Phi]1^2 + ( 19353600 $CellContext`c) $CellContext`h\[Phi]1^3 - 212889600 $CellContext`h\[Phi]1^4) $CellContext`L2^8)) Pi^8}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.704042631409958*^9, 3.704042659643123*^9}, 3.7041200337358904`*^9, 3.7041200746500072`*^9, {3.704124558584817*^9, 3.7041245601233606`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["S_2(\[Rho]_A(L1,\[Phi]),\[Rho]_A(L2,q))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, 3.7041200258581767`*^9, { 3.7041200815416093`*^9, 3.7041200819048214`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"S2L1\[Phi]L2q", "=", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"4608", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "2"]}], RowBox[{"48", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "3"]}], RowBox[{"32", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}]}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "4"]}], RowBox[{"16", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 4608]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^4, 0, (((( Rational[ 1, 48]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((( Rational[ 1, 32]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((( Rational[ 1, 16]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-(-8 + $CellContext`c)) $CellContext`L1^2 + \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"240", " ", "h\[Phi]", " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{"11", " ", "c", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], "-", SuperscriptBox["L2", "4"]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"552960", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", "c", " ", RowBox[{"(", RowBox[{"33", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"10", " ", RowBox[{"(", RowBox[{"11", "+", RowBox[{"3", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"11", " ", "c"}], "-", RowBox[{"240", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "2"]}], RowBox[{"11520", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"319", "+", RowBox[{"80", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"10", " ", RowBox[{"(", RowBox[{"33", "+", RowBox[{"8", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"11", " ", "c"}], "-", RowBox[{"240", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "3"]}], RowBox[{"7680", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"11", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "160"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"9", "+", RowBox[{"10", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"10", " ", RowBox[{"(", RowBox[{"59", "+", RowBox[{"11", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"11", " ", "c"}], "-", RowBox[{"240", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "4"]}], RowBox[{"3840", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 552960]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) (( 240 $CellContext`h\[Phi]) $CellContext`L2^4 + ( 11 $CellContext`c) ($CellContext`L1^4 - $CellContext`L2^4))) Pi^6, 0, (((( Rational[ 1, 11520]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (((3 $CellContext`c) (33 + 10 $CellContext`c)) $CellContext`L1^4 - ((( 10 (11 + 3 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ (11 $CellContext`c - 240 $CellContext`h\[Phi]) $CellContext`L2^4)) Pi^6, (((( Rational[ 1, 7680]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (($CellContext`c (319 + 80 $CellContext`c)) $CellContext`L1^4 - ((( 10 (33 + 8 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ (11 $CellContext`c - 240 $CellContext`h\[Phi]) $CellContext`L2^4)) Pi^6, (((( Rational[ 1, 3840]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (( 11 (-160 + $CellContext`c (9 + 10 $CellContext`c))) $CellContext`L1^4 - ((( 10 (59 + 11 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ (11 $CellContext`c - 240 $CellContext`h\[Phi]) $CellContext`L2^4)) Pi^6}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{ FractionBox["1", RowBox[{"1238630400", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2153", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"1460", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"126", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"11", " ", "c"}], "-", RowBox[{"240", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "-", RowBox[{"20", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"73", " ", "c"}], "-", RowBox[{"1512", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2153", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"95520", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"967680", " ", "c", " ", RowBox[{"(", RowBox[{"24", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "+", RowBox[{"19353600", " ", "c", " ", SuperscriptBox["h\[Phi]", "3"]}], "-", RowBox[{"212889600", " ", SuperscriptBox["h\[Phi]", "4"]}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}]}], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"1963", "+", RowBox[{"1701", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"63", " ", RowBox[{"(", RowBox[{"41", "+", RowBox[{"30", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"63", " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"11", "+", RowBox[{"3", " ", "c"}]}], ")"}]}], "-", RowBox[{"80", " ", RowBox[{"(", RowBox[{"3", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"320", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "73"}], " ", "c"}], "+", RowBox[{"1512", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"1290240", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"21157", "+", RowBox[{"12376", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"7", " ", RowBox[{"(", RowBox[{"3309", "+", RowBox[{"1840", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"21", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", "c", " ", RowBox[{"(", RowBox[{"33", "+", RowBox[{"8", " ", "c"}]}], ")"}]}], "-", RowBox[{"80", " ", RowBox[{"(", RowBox[{"27", "+", RowBox[{"8", " ", "c"}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2560", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "73"}], " ", "c"}], "+", RowBox[{"1512", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"860160", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "+", RowBox[{ FractionBox["1", RowBox[{"430080", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "96768"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"14059", "+", RowBox[{"27237", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{"21", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"3563", "+", RowBox[{"1490", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"21", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"59", "+", RowBox[{"11", " ", "c"}]}], ")"}]}], "-", RowBox[{"80", " ", "c", " ", RowBox[{"(", RowBox[{"1046", "+", RowBox[{"55", " ", "c", " ", RowBox[{"(", RowBox[{"9", "+", "c"}], ")"}]}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"320", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "88"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"306", "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"73", " ", "c"}], "-", RowBox[{"1512", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((((Rational[1, 1238630400] $CellContext`c^(-2))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) \ (((2153 $CellContext`c^3) (22 + 5 $CellContext`c)) $CellContext`L1^8 - (((( 1460 $CellContext`c^2) (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^6) $CellContext`L2^2 - \ ((((126 $CellContext`c^2) (22 + 5 $CellContext`c)) (11 $CellContext`c - 240 $CellContext`h\[Phi])) $CellContext`L1^4) \ $CellContext`L2^4 - ((((20 $CellContext`c^2) (22 + 5 $CellContext`c)) ( 73 $CellContext`c - 1512 $CellContext`h\[Phi])) $CellContext`L1^2) \ $CellContext`L2^6 + ((2153 $CellContext`c^3) (22 + 5 $CellContext`c) - (( 95520 $CellContext`c^2) (22 + 5 $CellContext`c)) $CellContext`h\[Phi] + (( 967680 $CellContext`c) (24 + 5 $CellContext`c)) $CellContext`h\[Phi]^2 + ( 19353600 $CellContext`c) $CellContext`h\[Phi]^3 - 212889600 $CellContext`h\[Phi]^4) $CellContext`L2^8)) Pi^8, 0, ((((Rational[-1, 1290240]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c (1963 + 1701 $CellContext`c)) $CellContext`L1^6 - ((( 63 (41 + 30 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ ((63 ($CellContext`c (11 + 3 $CellContext`c) - ( 80 (3 + $CellContext`c)) $CellContext`h\[Phi] + 320 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ((-73) $CellContext`c + 1512 $CellContext`h\[Phi]) $CellContext`L2^6)) Pi^8, (((( Rational[-1, 860160]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c (21157 + 12376 $CellContext`c)) $CellContext`L1^6 - ((( 7 (3309 + 1840 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ ((21 ((3 $CellContext`c) (33 + 8 $CellContext`c) - ( 80 (27 + 8 $CellContext`c)) $CellContext`h\[Phi] + 2560 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ((-73) $CellContext`c + 1512 $CellContext`h\[Phi]) $CellContext`L2^6)) Pi^8, (((((Rational[1, 430080] $CellContext`c^(-2))/(22 + 5 $CellContext`c)) $CellContext`L1^(-6)) $CellContext`L2^(-8)) \ ((((-$CellContext`c) (22 + 5 $CellContext`c)) (-96768 + $CellContext`c (14059 + 27237 $CellContext`c))) $CellContext`L1^6 + ((((( 21 $CellContext`c) (22 + 5 $CellContext`c)) (3563 + 1490 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) \ $CellContext`L2^2 - (( 21 (((3 $CellContext`c^2) (22 + 5 $CellContext`c)) (59 + 11 $CellContext`c) - ((80 $CellContext`c) ( 1046 + (55 $CellContext`c) ( 9 + $CellContext`c))) $CellContext`h\[Phi] + ( 320 (-88 + $CellContext`c (306 + 55 $CellContext`c))) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^4 + (($CellContext`c (22 + 5 $CellContext`c)) (73 $CellContext`c - 1512 $CellContext`h\[Phi])) $CellContext`L2^6)) Pi^8}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, {((((Rational[ 1, 4608]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^4, 0, ((((Rational[ 1, 48]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((( Rational[ 1, 32]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((( Rational[ 1, 16]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-(-8 + $CellContext`c)) $CellContext`L1^2 + \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 552960]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) (( 240 $CellContext`h\[Phi]) $CellContext`L2^4 + ( 11 $CellContext`c) ($CellContext`L1^4 - $CellContext`L2^4))) Pi^6, 0, ((((Rational[ 1, 11520]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (((3 $CellContext`c) (33 + 10 $CellContext`c)) $CellContext`L1^4 - ((( 10 (11 + 3 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ (11 $CellContext`c - 240 $CellContext`h\[Phi]) $CellContext`L2^4)) Pi^6, (((( Rational[ 1, 7680]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (($CellContext`c (319 + 80 $CellContext`c)) $CellContext`L1^4 - ((( 10 (33 + 8 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ (11 $CellContext`c - 240 $CellContext`h\[Phi]) $CellContext`L2^4)) Pi^6, (((( Rational[ 1, 3840]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (( 11 (-160 + $CellContext`c (9 + 10 $CellContext`c))) $CellContext`L1^4 - ((( 10 (59 + 11 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ (11 $CellContext`c - 240 $CellContext`h\[Phi]) $CellContext`L2^4)) Pi^6}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {(((((Rational[1, 1238630400] $CellContext`c^(-2))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) ((( 2153 $CellContext`c^3) (22 + 5 $CellContext`c)) $CellContext`L1^8 - (((( 1460 $CellContext`c^2) (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^6) $CellContext`L2^2 - \ ((((126 $CellContext`c^2) (22 + 5 $CellContext`c)) (11 $CellContext`c - 240 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^4 - \ ((((20 $CellContext`c^2) (22 + 5 $CellContext`c)) (73 $CellContext`c - 1512 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^6 + \ ((2153 $CellContext`c^3) (22 + 5 $CellContext`c) - ((95520 $CellContext`c^2) ( 22 + 5 $CellContext`c)) $CellContext`h\[Phi] + (( 967680 $CellContext`c) (24 + 5 $CellContext`c)) $CellContext`h\[Phi]^2 + ( 19353600 $CellContext`c) $CellContext`h\[Phi]^3 - 212889600 $CellContext`h\[Phi]^4) $CellContext`L2^8)) Pi^8, 0, ((((Rational[-1, 1290240]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c (1963 + 1701 $CellContext`c)) $CellContext`L1^6 - ((( 63 (41 + 30 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ ((63 ($CellContext`c (11 + 3 $CellContext`c) - ( 80 (3 + $CellContext`c)) $CellContext`h\[Phi] + 320 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ((-73) $CellContext`c + 1512 $CellContext`h\[Phi]) $CellContext`L2^6)) Pi^8, (((( Rational[-1, 860160]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c (21157 + 12376 $CellContext`c)) $CellContext`L1^6 - ((( 7 (3309 + 1840 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ ((21 ((3 $CellContext`c) (33 + 8 $CellContext`c) - ( 80 (27 + 8 $CellContext`c)) $CellContext`h\[Phi] + 2560 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ((-73) $CellContext`c + 1512 $CellContext`h\[Phi]) $CellContext`L2^6)) Pi^8, (((((Rational[1, 430080] $CellContext`c^(-2))/(22 + 5 $CellContext`c)) $CellContext`L1^(-6)) $CellContext`L2^(-8)) \ ((((-$CellContext`c) (22 + 5 $CellContext`c)) (-96768 + $CellContext`c (14059 + 27237 $CellContext`c))) $CellContext`L1^6 + ((((( 21 $CellContext`c) (22 + 5 $CellContext`c)) (3563 + 1490 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 - \ ((21 (((3 $CellContext`c^2) (22 + 5 $CellContext`c)) (59 + 11 $CellContext`c) - ((80 $CellContext`c) ( 1046 + (55 $CellContext`c) ( 9 + $CellContext`c))) $CellContext`h\[Phi] + ( 320 (-88 + $CellContext`c (306 + 55 $CellContext`c))) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^4 + (($CellContext`c (22 + 5 $CellContext`c)) (73 $CellContext`c - 1512 $CellContext`h\[Phi])) $CellContext`L2^6)) Pi^8}, 0, 5, 1]}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.7041154839401503`*^9, 3.7041155058482423`*^9}, 3.7041200391757126`*^9, 3.70412009230025*^9, {3.7041249457334986`*^9, 3.704124946982025*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["S_2(\[Rho]_A(L1,q1),\[Rho]_A(L2,q2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, {3.704116595159308*^9, 3.704116597929334*^9}, {3.7041177049986935`*^9, 3.704117707948104*^9}, 3.704120028560308*^9, {3.704120086479438*^9, 3.7041200867951765`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"S2L1q1L2q2", "=", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"4608", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"48", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"32", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"8", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}], "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "4"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"16", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 4608] $CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) ($CellContext`L1^2 - $CellContext`L2^2)^2) Pi^4, 0, (((((Rational[-1, 48] $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^2 + $CellContext`L1^2 \ $CellContext`q2^2), ((((( Rational[-1, 32] $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^3 + $CellContext`L1^2 \ $CellContext`q2^3), (((( Rational[ 1, 16]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) Pi^4) ( 8 ($CellContext`L2^2 $CellContext`q1^2 - $CellContext`L1^2 \ $CellContext`q2^2)^2 + (($CellContext`c ($CellContext`L1 - $CellContext`L2)) \ ($CellContext`L1 + $CellContext`L2)) ($CellContext`L2^2 $CellContext`q1^4 - \ $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"11", " ", "c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "+", SuperscriptBox["L2", "2"]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"552960", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", RowBox[{"(", RowBox[{"33", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "4"], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{"3", " ", RowBox[{"(", RowBox[{"33", "+", RowBox[{"10", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{"11", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{"q1", "-", "q2"}], ")"}], " ", RowBox[{"(", RowBox[{"q1", "+", "q2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"11520", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"319", "+", RowBox[{"80", " ", "c"}]}], ")"}]}], " ", SuperscriptBox["L2", "4"], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"319", "+", RowBox[{"80", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["q2", "3"]}], "+", RowBox[{"11", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q1", "3"], "-", SuperscriptBox["q2", "3"]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"7680", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"3840", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], RowBox[{ SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"11", " ", "c", " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"10", " ", "c", " ", RowBox[{"(", RowBox[{"59", "+", RowBox[{"11", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"11", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "160"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"9", "+", RowBox[{"10", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "+", RowBox[{"160", " ", RowBox[{"(", RowBox[{"11", "+", RowBox[{"3", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "+", SuperscriptBox["L2", "2"]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"11", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "160"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"9", "+", RowBox[{"10", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"10", " ", "c", " ", RowBox[{"(", RowBox[{"59", "+", RowBox[{"11", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"11", " ", "c", " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((( Rational[ 11, 552960] $CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`L1^2 - $CellContext`L2^2)^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) Pi^6, 0, (((((Rational[ 1, 11520] $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) ((((-3) (33 + 10 $CellContext`c)) $CellContext`L2^4) $CellContext`q1^2 + (( 3 (33 + 10 $CellContext`c)) $CellContext`L1^4) \ $CellContext`q2^2 + ((( 11 $CellContext`L1^2) $CellContext`L2^2) ($CellContext`q1 - \ $CellContext`q2)) ($CellContext`q1 + $CellContext`q2)), ((((( Rational[ 1, 7680] $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-(319 + 80 $CellContext`c)) $CellContext`L2^4) $CellContext`q1^3 + (( 319 + 80 $CellContext`c) $CellContext`L1^4) $CellContext`q2^3 + \ ((11 $CellContext`L1^2) $CellContext`L2^2) ($CellContext`q1^3 - \ $CellContext`q2^3)), (((( Rational[ 1, 3840]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) Pi^6) (($CellContext`L2^2 (( 11 $CellContext`c) $CellContext`L1^4 - (((10 $CellContext`c) ( 59 + 11 $CellContext`c)) $CellContext`L1^2) \ $CellContext`L2^2 + ( 11 (-160 + $CellContext`c (9 + 10 $CellContext`c))) $CellContext`L2^4)) $CellContext`q1^4 + \ (((((160 (11 + 3 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) $CellContext`q1^2) $CellContext`q2^2 + \ ($CellContext`L1^2 (( 11 (-160 + $CellContext`c (9 + 10 $CellContext`c))) $CellContext`L1^4 - ((( 10 $CellContext`c) (59 + 11 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + ( 11 $CellContext`c) $CellContext`L2^4)) $CellContext`q2^4)}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"2153", " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"2846", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"2153", " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"1238630400", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1963", "+", RowBox[{"1701", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"1963", "+", RowBox[{"1701", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"620", "+", RowBox[{"189", " ", "c"}]}], ")"}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{"73", " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"73", " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"620", "+", RowBox[{"189", " ", "c"}]}], ")"}], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"1290240", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"860160", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"21157", "+", RowBox[{"12376", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "3"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"21157", "+", RowBox[{"12376", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "3"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"2006", "+", RowBox[{"504", " ", "c"}]}], ")"}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{"73", " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"73", " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"1003", "+", RowBox[{"252", " ", "c"}]}], ")"}], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "3"]}]}], "+", RowBox[{ FractionBox["1", RowBox[{"430080", " ", "c", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"73", " ", "c", " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"63", " ", "c", " ", RowBox[{"(", RowBox[{"59", "+", RowBox[{"11", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"21", " ", "c", " ", RowBox[{"(", RowBox[{"3563", "+", RowBox[{"1490", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"96768", "-", RowBox[{"c", " ", RowBox[{"(", RowBox[{"14059", "+", RowBox[{"27237", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{"336", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", RowBox[{"(", RowBox[{"41", "+", RowBox[{"30", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"10", " ", RowBox[{"(", RowBox[{"33", "+", RowBox[{"2", " ", "c", " ", RowBox[{"(", RowBox[{"8", "+", "c"}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"3", " ", RowBox[{"(", RowBox[{"41", "+", RowBox[{"30", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"96768", "-", RowBox[{"c", " ", RowBox[{"(", RowBox[{"14059", "+", RowBox[{"27237", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{"21", " ", "c", " ", RowBox[{"(", RowBox[{"3563", "+", RowBox[{"1490", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"63", " ", "c", " ", RowBox[{"(", RowBox[{"59", "+", RowBox[{"11", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{"73", " ", "c", " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 1238630400] $CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) ($CellContext`L1^2 - $CellContext`L2^2)^2) ( 2153 $CellContext`L1^4 + ( 2846 $CellContext`L1^2) $CellContext`L2^2 + 2153 $CellContext`L2^4)) Pi^8, 0, (((((Rational[ 1, 1290240] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) (((1963 + 1701 $CellContext`c) $CellContext`L2^6) $CellContext`q1^2 - (( 1963 + 1701 $CellContext`c) $CellContext`L1^6) $CellContext`q2^2 - \ ($CellContext`L1^2 $CellContext`L2^4) ((620 + 189 $CellContext`c) $CellContext`q1^2 + 73 $CellContext`q2^2) + ($CellContext`L1^4 $CellContext`L2^2) ( 73 $CellContext`q1^2 + (620 + 189 $CellContext`c) $CellContext`q2^2)), ((((( Rational[ 1, 860160] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) (((21157 + 12376 $CellContext`c) $CellContext`L2^6) $CellContext`q1^3 - (( 21157 + 12376 $CellContext`c) $CellContext`L1^6) \ $CellContext`q2^3 - ($CellContext`L1^2 $CellContext`L2^4) ((2006 + 504 $CellContext`c) $CellContext`q1^3 + 73 $CellContext`q2^3) + ($CellContext`L1^4 $CellContext`L2^2) ( 73 $CellContext`q1^3 + ( 2 (1003 + 252 $CellContext`c)) $CellContext`q2^3)), (((( Rational[ 1, 430080]/$CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) Pi^8) (($CellContext`L2^2 (( 73 $CellContext`c) $CellContext`L1^6 - (((63 $CellContext`c) ( 59 + 11 $CellContext`c)) $CellContext`L1^4) \ $CellContext`L2^2 + (((21 $CellContext`c) (3563 + 1490 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^4 + \ (96768 - $CellContext`c (14059 + 27237 $CellContext`c)) $CellContext`L2^6)) $CellContext`q1^4 - \ ((((336 $CellContext`L1^2) $CellContext`L2^2) (( 3 (41 + 30 $CellContext`c)) $CellContext`L1^4 + (( 10 (33 + (2 $CellContext`c) ( 8 + $CellContext`c))) $CellContext`L1^2) \ $CellContext`L2^2 + ( 3 (41 + 30 $CellContext`c)) $CellContext`L2^4)) $CellContext`q1^2) \ $CellContext`q2^2 + ($CellContext`L1^2 (( 96768 - $CellContext`c (14059 + 27237 $CellContext`c)) $CellContext`L1^6 + ((( 21 $CellContext`c) (3563 + 1490 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^2 - \ (((63 $CellContext`c) (59 + 11 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^4 + ( 73 $CellContext`c) $CellContext`L2^6)) $CellContext`q2^4)}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, {((((Rational[ 1, 4608] $CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) ($CellContext`L1^2 - $CellContext`L2^2)^2) Pi^4, 0, (((((Rational[-1, 48] $CellContext`L1^(-4)) ($CellContext`L1 - $CellContext`L2)) \ $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^2 + $CellContext`L1^2 \ $CellContext`q2^2), ((((( Rational[-1, 32] $CellContext`L1^(-4)) ($CellContext`L1 - $CellContext`L2)) \ $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^3 + $CellContext`L1^2 \ $CellContext`q2^3), (((( Rational[ 1, 16]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) Pi^4) ( 8 ($CellContext`L2^2 $CellContext`q1^2 - $CellContext`L1^2 \ $CellContext`q2^2)^2 + (($CellContext`c ($CellContext`L1 - $CellContext`L2)) \ ($CellContext`L1 + $CellContext`L2)) ($CellContext`L2^2 $CellContext`q1^4 - \ $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((( Rational[ 11, 552960] $CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`L1^2 - $CellContext`L2^2)^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) Pi^6, 0, (((((Rational[ 1, 11520] $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) ((((-3) (33 + 10 $CellContext`c)) $CellContext`L2^4) $CellContext`q1^2 + (( 3 (33 + 10 $CellContext`c)) $CellContext`L1^4) $CellContext`q2^2 + \ (((11 $CellContext`L1^2) $CellContext`L2^2) ($CellContext`q1 - \ $CellContext`q2)) ($CellContext`q1 + $CellContext`q2)), ((((( Rational[ 1, 7680] $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-(319 + 80 $CellContext`c)) $CellContext`L2^4) $CellContext`q1^3 + ((319 + 80 $CellContext`c) $CellContext`L1^4) $CellContext`q2^3 + (( 11 $CellContext`L1^2) $CellContext`L2^2) ($CellContext`q1^3 - \ $CellContext`q2^3)), (((( Rational[ 1, 3840]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) Pi^6) (($CellContext`L2^2 (( 11 $CellContext`c) $CellContext`L1^4 - (((10 $CellContext`c) ( 59 + 11 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + \ (11 (-160 + $CellContext`c (9 + 10 $CellContext`c))) $CellContext`L2^4)) $CellContext`q1^4 + \ (((((160 (11 + 3 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) $CellContext`q1^2) $CellContext`q2^2 + \ ($CellContext`L1^2 (( 11 (-160 + $CellContext`c (9 + 10 $CellContext`c))) $CellContext`L1^4 - ((( 10 $CellContext`c) (59 + 11 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + ( 11 $CellContext`c) $CellContext`L2^4)) $CellContext`q2^4)}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 1238630400] $CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) ($CellContext`L1^2 - $CellContext`L2^2)^2) ( 2153 $CellContext`L1^4 + (2846 $CellContext`L1^2) $CellContext`L2^2 + 2153 $CellContext`L2^4)) Pi^8, 0, (((((Rational[ 1, 1290240] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) (((1963 + 1701 $CellContext`c) $CellContext`L2^6) $CellContext`q1^2 - (( 1963 + 1701 $CellContext`c) $CellContext`L1^6) $CellContext`q2^2 - \ ($CellContext`L1^2 $CellContext`L2^4) ((620 + 189 $CellContext`c) $CellContext`q1^2 + 73 $CellContext`q2^2) + ($CellContext`L1^4 $CellContext`L2^2) ( 73 $CellContext`q1^2 + (620 + 189 $CellContext`c) $CellContext`q2^2)), ((((( Rational[ 1, 860160] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) (((21157 + 12376 $CellContext`c) $CellContext`L2^6) $CellContext`q1^3 - (( 21157 + 12376 $CellContext`c) $CellContext`L1^6) $CellContext`q2^3 - \ ($CellContext`L1^2 $CellContext`L2^4) ((2006 + 504 $CellContext`c) $CellContext`q1^3 + 73 $CellContext`q2^3) + ($CellContext`L1^4 $CellContext`L2^2) ( 73 $CellContext`q1^3 + ( 2 (1003 + 252 $CellContext`c)) $CellContext`q2^3)), (((( Rational[ 1, 430080]/$CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) Pi^8) (($CellContext`L2^2 (( 73 $CellContext`c) $CellContext`L1^6 - (((63 $CellContext`c) ( 59 + 11 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^2 + \ (((21 $CellContext`c) (3563 + 1490 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^4 + ( 96768 - $CellContext`c (14059 + 27237 $CellContext`c)) $CellContext`L2^6)) $CellContext`q1^4 - \ ((((336 $CellContext`L1^2) $CellContext`L2^2) (( 3 (41 + 30 $CellContext`c)) $CellContext`L1^4 + (( 10 (33 + (2 $CellContext`c) ( 8 + $CellContext`c))) $CellContext`L1^2) $CellContext`L2^2 + \ (3 (41 + 30 $CellContext`c)) $CellContext`L2^4)) $CellContext`q1^2) \ $CellContext`q2^2 + ($CellContext`L1^2 (( 96768 - $CellContext`c (14059 + 27237 $CellContext`c)) $CellContext`L1^6 + ((( 21 $CellContext`c) (3563 + 1490 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^2 - \ (((63 $CellContext`c) (59 + 11 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^4 + ( 73 $CellContext`c) $CellContext`L2^6)) $CellContext`q2^4)}, 0, 5, 1]}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.7041177096676693`*^9, 3.704117722947776*^9}, 3.7041200520732484`*^9, 3.7041200892496595`*^9, {3.7041256489764595`*^9, 3.7041256504155164`*^9}}] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Section 3.2 Jensen-Shannon divergence", "Section", CellChangeTimes->{{3.7039542022131257`*^9, 3.703954219345484*^9}, { 3.7039553305656457`*^9, 3.703955332918915*^9}, {3.704042560801203*^9, 3.704042566640339*^9}, {3.704120014430778*^9, 3.704120020367242*^9}, { 3.704120063669981*^9, 3.7041200710617695`*^9}, 3.7041202585198755`*^9, { 3.704126824559267*^9, 3.704126842406231*^9}, 3.7041729013023696`*^9, { 3.7118130772234983`*^9, 3.7118130881920424`*^9}}], Cell[CellGroupData[{ Cell["JS(\[Rho]_A(L1,\[Phi]1),\[Rho]_A(L2,\[Phi]2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, 3.704120023776886*^9, {3.704120076714172*^9, 3.704120078900853*^9}, { 3.704126845060828*^9, 3.7041268452944665`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"JSL1\[Phi]1L2\[Phi]2", "=", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["\[ScriptL]", "4"]}], RowBox[{"4320", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["\[ScriptL]", "6"]}], RowBox[{"45360", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"65318400", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "25"}], " ", SuperscriptBox["c", "6"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "4"]}], "+", RowBox[{"291962880", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"h\[Phi]2", " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{"h\[Phi]1", " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"7", " ", SuperscriptBox["h\[Phi]2", "2"], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"10", " ", "h\[Phi]1", " ", "h\[Phi]2", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"7", " ", SuperscriptBox["h\[Phi]1", "2"], " ", SuperscriptBox["L2", "4"]}]}], ")"}]}], "+", RowBox[{"10", " ", SuperscriptBox["c", "5"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"41", "+", RowBox[{"240", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "67"}], "+", RowBox[{"120", " ", "h\[Phi]1"}], "+", RowBox[{"120", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"41", "+", RowBox[{"240", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}]}], "-", RowBox[{"16", " ", SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "143"}], "+", RowBox[{"60", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{"53", "+", RowBox[{"90", " ", "h\[Phi]2"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"15", " ", RowBox[{"(", RowBox[{"11", "+", RowBox[{"8", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "34"}], "+", RowBox[{"45", " ", "h\[Phi]2"}]}], ")"}]}], "+", RowBox[{"h\[Phi]1", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "52"}], "+", RowBox[{"720", " ", "h\[Phi]2"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"15", " ", RowBox[{"(", RowBox[{"11", "-", RowBox[{"52", " ", "h\[Phi]2"}], "+", RowBox[{"8", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "34"}], "+", RowBox[{"45", " ", "h\[Phi]1"}], "+", RowBox[{"90", " ", "h\[Phi]2"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"143", "-", RowBox[{"60", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{"53", "+", RowBox[{"90", " ", "h\[Phi]1"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}]}], "+", RowBox[{"1105920", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["h\[Phi]2", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "242"}], "+", RowBox[{"255", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "+", RowBox[{"4", " ", SuperscriptBox["h\[Phi]2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"h\[Phi]1", " ", RowBox[{"(", RowBox[{"22", "-", RowBox[{"27", " ", "h\[Phi]2"}]}], ")"}]}], "+", RowBox[{"11", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"2", " ", "h\[Phi]1", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{ RowBox[{"h\[Phi]1", " ", RowBox[{"(", RowBox[{"55", "-", RowBox[{"147", " ", "h\[Phi]2"}]}], ")"}]}], "+", RowBox[{"55", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{"4", " ", SuperscriptBox["h\[Phi]1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"h\[Phi]1", " ", RowBox[{"(", RowBox[{"11", "-", RowBox[{"27", " ", "h\[Phi]2"}]}], ")"}]}], "+", RowBox[{"22", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], "+", RowBox[{ SuperscriptBox["h\[Phi]1", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "242"}], "+", RowBox[{"255", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}]}], "-", RowBox[{"9216", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["h\[Phi]2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1387"}], "+", RowBox[{"900", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{"5", "+", "h\[Phi]2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"2", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{ RowBox[{"10", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "22"}], "+", RowBox[{"27", " ", "h\[Phi]2"}]}], ")"}]}], "+", RowBox[{"3", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{"3", "+", RowBox[{"10", " ", "h\[Phi]2"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "11"}], "+", RowBox[{"60", " ", "h\[Phi]2"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"60", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{"18", "-", RowBox[{"59", " ", "h\[Phi]2"}]}], ")"}], " ", "h\[Phi]2"}], "+", RowBox[{"209", " ", SuperscriptBox["h\[Phi]2", "2"]}], "+", RowBox[{ SuperscriptBox["h\[Phi]1", "2"], " ", RowBox[{"(", RowBox[{"209", "+", RowBox[{"60", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "59"}], "+", RowBox[{"90", " ", "h\[Phi]2"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "-", RowBox[{"2", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "99"}], " ", "h\[Phi]2"}], "+", RowBox[{"10", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "22"}], "+", RowBox[{"21", " ", "h\[Phi]2"}], "+", RowBox[{"9", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{"3", "+", RowBox[{"20", " ", "h\[Phi]2"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], "+", RowBox[{ SuperscriptBox["h\[Phi]1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1387"}], "+", RowBox[{"900", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{"5", "+", "h\[Phi]1"}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}]}], "+", RowBox[{"768", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"h\[Phi]2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "352"}], "+", RowBox[{"15", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{"193", "+", RowBox[{"120", " ", "h\[Phi]2"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{"3", "+", RowBox[{"10", " ", "h\[Phi]2"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "11"}], "+", RowBox[{"60", " ", "h\[Phi]2"}]}], ")"}]}], "+", RowBox[{"h\[Phi]1", " ", RowBox[{"(", RowBox[{"11", "+", RowBox[{"450", " ", "h\[Phi]2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"12", " ", "h\[Phi]2"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"3", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"88", "-", RowBox[{"355", " ", "h\[Phi]1"}]}], ")"}], " ", "h\[Phi]1"}], "+", RowBox[{"88", " ", "h\[Phi]2"}], "+", RowBox[{"60", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "23"}], "+", RowBox[{"30", " ", "h\[Phi]1"}]}], ")"}], " ", "h\[Phi]2"}], "+", RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "71"}], "+", RowBox[{"360", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["h\[Phi]2", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"11", " ", "h\[Phi]2"}], "+", RowBox[{"3", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", RowBox[{"(", RowBox[{"11", "+", RowBox[{"50", " ", "h\[Phi]2"}]}], ")"}]}], "+", RowBox[{"10", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{"7", "+", RowBox[{"60", " ", "h\[Phi]1"}], "+", RowBox[{"180", " ", "h\[Phi]2"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], "+", RowBox[{"h\[Phi]1", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "352"}], "+", RowBox[{"15", " ", "h\[Phi]1", " ", RowBox[{"(", RowBox[{"193", "+", RowBox[{"120", " ", "h\[Phi]1"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["\[ScriptL]", "8"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, {((((Rational[ 1, 4320]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)^2) Pi^4, 0, (((((Rational[ 1, 45360] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)^2) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)) Pi^6, 0, (((((Rational[1, 65318400] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) \ (((-25) $CellContext`c^6) ($CellContext`L1^2 - $CellContext`L2^2)^4 + ( 291962880 ($CellContext`h\[Phi]2 $CellContext`L1^2 - $CellContext`h\ \[Phi]1 $CellContext`L2^2)^2) (( 7 $CellContext`h\[Phi]2^2) $CellContext`L1^4 + ((( 10 $CellContext`h\[Phi]1) $CellContext`h\[Phi]2) \ $CellContext`L1^2) $CellContext`L2^2 + ( 7 $CellContext`h\[Phi]1^2) $CellContext`L2^4) + (( 10 $CellContext`c^5) ($CellContext`L1^2 - $CellContext`L2^2)^2) (( 41 + 240 $CellContext`h\[Phi]2) $CellContext`L1^4 - (( 2 (-67 + 120 $CellContext`h\[Phi]1 + 120 $CellContext`h\[Phi]2)) $CellContext`L1^2) $CellContext`L2^2 + \ (41 + 240 $CellContext`h\[Phi]1) $CellContext`L2^4) - ((( 16 $CellContext`c^4) ($CellContext`L1 - $CellContext`L2)) \ ($CellContext`L1 + $CellContext`L2)) ((-143 + (60 $CellContext`h\[Phi]2) (53 + 90 $CellContext`h\[Phi]2)) $CellContext`L1^6 - (( 15 (11 + (8 $CellContext`h\[Phi]2) (-34 + 45 $CellContext`h\[Phi]2) + $CellContext`h\[Phi]1 (-52 + 720 $CellContext`h\[Phi]2))) $CellContext`L1^4) \ $CellContext`L2^2 + (( 15 (11 - 52 $CellContext`h\[Phi]2 + ( 8 $CellContext`h\[Phi]1) (-34 + 45 $CellContext`h\[Phi]1 + 90 $CellContext`h\[Phi]2))) $CellContext`L1^2) \ $CellContext`L2^4 + ( 143 - (60 $CellContext`h\[Phi]1) (53 + 90 $CellContext`h\[Phi]1)) $CellContext`L2^6) + ( 1105920 $CellContext`c) (($CellContext`h\[Phi]2^3 (-242 + 255 $CellContext`h\[Phi]2)) $CellContext`L1^8 + ((( 4 $CellContext`h\[Phi]2^2) ($CellContext`h\[Phi]1 (22 - 27 $CellContext`h\[Phi]2) + 11 $CellContext`h\[Phi]2)) $CellContext`L1^6) $CellContext`L2^2 + \ ((((2 $CellContext`h\[Phi]1) $CellContext`h\[Phi]2) ($CellContext`h\[Phi]1 ( 55 - 147 $CellContext`h\[Phi]2) + 55 $CellContext`h\[Phi]2)) $CellContext`L1^4) $CellContext`L2^4 + \ (((4 $CellContext`h\[Phi]1^2) ($CellContext`h\[Phi]1 (11 - 27 $CellContext`h\[Phi]2) + 22 $CellContext`h\[Phi]2)) $CellContext`L1^2) $CellContext`L2^6 + \ ($CellContext`h\[Phi]1^3 (-242 + 255 $CellContext`h\[Phi]1)) $CellContext`L2^8) - ( 9216 $CellContext`c^2) (($CellContext`h\[Phi]2^2 (-1387 + ( 900 $CellContext`h\[Phi]2) ( 5 + $CellContext`h\[Phi]2))) $CellContext`L1^8 - ((( 2 $CellContext`h\[Phi]2) ((10 $CellContext`h\[Phi]2) (-22 + 27 $CellContext`h\[Phi]2) + ((3 $CellContext`h\[Phi]1) (3 + 10 $CellContext`h\[Phi]2)) (-11 + 60 $CellContext`h\[Phi]2))) $CellContext`L1^6) \ $CellContext`L2^2 + ((((60 $CellContext`h\[Phi]1) (18 - 59 $CellContext`h\[Phi]2)) $CellContext`h\[Phi]2 + 209 $CellContext`h\[Phi]2^2 + $CellContext`h\[Phi]1^2 ( 209 + (60 $CellContext`h\[Phi]2) (-59 + 90 $CellContext`h\[Phi]2))) $CellContext`L1^4) \ $CellContext`L2^4 - ((( 2 $CellContext`h\[Phi]1) ((-99) $CellContext`h\[Phi]2 + ( 10 $CellContext`h\[Phi]1) (-22 + 21 $CellContext`h\[Phi]2 + (9 $CellContext`h\[Phi]1) (3 + 20 $CellContext`h\[Phi]2)))) $CellContext`L1^2) \ $CellContext`L2^6 + ($CellContext`h\[Phi]1^2 (-1387 + ( 900 $CellContext`h\[Phi]1) ( 5 + $CellContext`h\[Phi]1))) $CellContext`L2^8) + ( 768 $CellContext`c^3) (($CellContext`h\[Phi]2 (-352 + ( 15 $CellContext`h\[Phi]2) (193 + 120 $CellContext`h\[Phi]2))) $CellContext`L1^8 - (((( 3 $CellContext`h\[Phi]2) (3 + 10 $CellContext`h\[Phi]2)) (-11 + 60 $CellContext`h\[Phi]2) + $CellContext`h\[Phi]1 ( 11 + (450 $CellContext`h\[Phi]2) (-1 + 12 $CellContext`h\[Phi]2))) $CellContext`L1^6) \ $CellContext`L2^2 + (( 3 ((88 - 355 $CellContext`h\[Phi]1) $CellContext`h\[Phi]1 + 88 $CellContext`h\[Phi]2 + ((60 $CellContext`h\[Phi]1) (-23 + 30 $CellContext`h\[Phi]1)) $CellContext`h\[Phi]2 + ( 5 (-71 + 360 $CellContext`h\[Phi]1)) $CellContext`h\[Phi]2^2)) \ $CellContext`L1^4) $CellContext`L2^4 - (( 11 $CellContext`h\[Phi]2 + ( 3 $CellContext`h\[Phi]1) ((-3) (11 + 50 $CellContext`h\[Phi]2) + (10 $CellContext`h\[Phi]1) (7 + 60 $CellContext`h\[Phi]1 + 180 $CellContext`h\[Phi]2))) $CellContext`L1^2) \ $CellContext`L2^6 + ($CellContext`h\[Phi]1 (-352 + ( 15 $CellContext`h\[Phi]1) (193 + 120 $CellContext`h\[Phi]1))) $CellContext`L2^8))) Pi^8}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.704042631409958*^9, 3.704042659643123*^9}, 3.7041200337358904`*^9, 3.7041200746500072`*^9, {3.704124558584817*^9, 3.7041245601233606`*^9}, {3.704126857355027*^9, 3.7041269027230988`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["JS(\[Rho]_A(L1,\[Phi]),\[Rho]_A(L2,q))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, 3.7041200258581767`*^9, { 3.7041200815416093`*^9, 3.7041200819048214`*^9}, 3.704126849767155*^9}], Cell[BoxData[ RowBox[{ RowBox[{"JSL1\[Phi]L2q", "=", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"4320", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "3"]}], RowBox[{"30", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}]}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 4320]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^4, 0, (((( Rational[ 1, 45]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((( Rational[ 1, 30]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((( Rational[ 1, 15]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-(-8 + $CellContext`c)) $CellContext`L1^2 + \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"45360", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", "c", " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"3", " ", "c", " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"630", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", "c", " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], "2"], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "4"]}], RowBox[{"315", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 45360] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`c $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^6, 0, ((((( Rational[-1, 945] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((3 $CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, ((((( Rational[-1, 630] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((3 $CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, (((( Rational[ 1, 315] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((((-3) (-16 + $CellContext`c)) $CellContext`c) \ $CellContext`L1^4 + (((2 (-8 + $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) \ $CellContext`L2^2 + ($CellContext`c - 24 $CellContext`h\[Phi])^2 $CellContext`L2^4)) Pi^6}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{ FractionBox["1", RowBox[{"65318400", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["c", "4"]}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "104"}], "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"]}], "+", RowBox[{"4", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"6", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"5", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"8", "+", "c"}], ")"}]}], "-", RowBox[{"48", " ", "c", " ", RowBox[{"(", RowBox[{"32", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"192", " ", RowBox[{"(", RowBox[{"76", "+", RowBox[{"15", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{"4", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", "c"}], ")"}], " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["c", "4"]}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "104"}], "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "+", RowBox[{"96", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "128"}], "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]"}], "-", RowBox[{"1152", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "11096"}], "+", RowBox[{"5", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "386"}], "+", RowBox[{"15", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "+", RowBox[{"276480", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "968"}], "+", RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "30"}], "+", "c"}], ")"}], " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}], "-", RowBox[{"1658880", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1232"}], "+", RowBox[{"5", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "34"}], "+", "c"}], ")"}], " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "4"]}]}], ")"}], " ", SuperscriptBox["L2", "8"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}]}], "-", RowBox[{ FractionBox["1", RowBox[{"340200", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"368", "+", RowBox[{"55", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"3", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"172", "+", RowBox[{"35", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"9", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"16", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "+", RowBox[{"80", " ", RowBox[{"(", RowBox[{"8", "-", RowBox[{"3", " ", "c"}]}], ")"}], " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"320", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "68"}], "+", RowBox[{"9", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", "c"}], ")"}], " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "2"]}]}], "-", RowBox[{ FractionBox["1", RowBox[{"226800", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"808", "+", RowBox[{"155", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"1396", "+", RowBox[{"305", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"145", " ", SuperscriptBox["c", "3"]}], "+", RowBox[{"8", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"73", "-", RowBox[{"870", " ", "h\[Phi]"}]}], ")"}]}], "-", RowBox[{"449280", " ", SuperscriptBox["h\[Phi]", "2"]}], "+", RowBox[{"960", " ", "c", " ", "h\[Phi]", " ", RowBox[{"(", RowBox[{"8", "+", RowBox[{"87", " ", "h\[Phi]"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", "c"}], ")"}], " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "3"]}]}], "-", RowBox[{ FractionBox["1", RowBox[{"113400", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "61984"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "11992"}], "+", RowBox[{"215", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8960"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"756", "+", RowBox[{"425", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"608", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"1224", "+", RowBox[{"205", " ", "c"}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"240", " ", "c", " ", RowBox[{"(", RowBox[{"3520", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"32", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"1094", "+", RowBox[{"205", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", RowBox[{"(", RowBox[{"4224", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "4936"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"234", "+", RowBox[{"205", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "4"}], "+", "c"}], ")"}], " ", "c", " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((((Rational[1, 65318400] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) \ ((((-$CellContext`c^4) (-104 + 5 $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`L1^8 + ((((( 4 $CellContext`c^3) (4 + 5 $CellContext`c)) (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^6) \ $CellContext`L2^2 - ((((6 $CellContext`c^2) (22 + 5 $CellContext`c)) ((5 $CellContext`c^2) ( 8 + $CellContext`c) - ((48 $CellContext`c) (32 + 5 $CellContext`c)) $CellContext`h\[Phi] + ( 192 (76 + 15 $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^4) $CellContext`L2^4 + (((((4 $CellContext`c) (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 (4 + 5 $CellContext`c) - (( 240 (-4 + $CellContext`c)) $CellContext`c) $CellContext`h\ \[Phi] + ( 2880 (-8 + $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^6 + (((-$CellContext`c^4) (-104 + 5 $CellContext`c)) (22 + 5 $CellContext`c) + (((96 $CellContext`c^3) (-128 + 5 $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`h\[Phi] - (( 1152 $CellContext`c^2) (-11096 + (5 $CellContext`c) (-386 + 15 $CellContext`c))) $CellContext`h\[Phi]^2 + (( 276480 $CellContext`c) (-968 + ( 5 (-30 + $CellContext`c)) $CellContext`c)) $CellContext`h\ \[Phi]^3 - (1658880 (-1232 + ( 5 (-34 + $CellContext`c)) $CellContext`c)) $CellContext`h\ \[Phi]^4) $CellContext`L2^8)) Pi^8, 0, ((((Rational[-1, 340200] $CellContext`c^(-3)) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c^3 (368 + 55 $CellContext`c)) $CellContext`L1^6 - (((( 3 $CellContext`c^2) (172 + 35 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ (((9 $CellContext`c) ($CellContext`c^2 (16 + 5 $CellContext`c) + (( 80 (8 - 3 $CellContext`c)) $CellContext`c) $CellContext`h\[Phi] + \ (320 (-68 + 9 $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^4 + (($CellContext`c - 24 $CellContext`h\[Phi]) ($CellContext`c^2 (4 + 5 $CellContext`c) - (( 240 (-4 + $CellContext`c)) $CellContext`c) $CellContext`h\ \[Phi] + ( 2880 (-8 + $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L2^6)) Pi^8, (((( Rational[-1, 226800] $CellContext`c^(-3)) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c^3 (808 + 155 $CellContext`c)) $CellContext`L1^6 - ((($CellContext`c^2 ( 1396 + 305 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ (($CellContext`c ( 145 $CellContext`c^3 + (8 $CellContext`c^2) (73 - 870 $CellContext`h\[Phi]) - 449280 $CellContext`h\[Phi]^2 + (( 960 $CellContext`c) $CellContext`h\[Phi]) (8 + 87 $CellContext`h\[Phi]))) $CellContext`L1^2) \ $CellContext`L2^4 + (($CellContext`c - 24 $CellContext`h\[Phi]) ($CellContext`c^2 (4 + 5 $CellContext`c) - (( 240 (-4 + $CellContext`c)) $CellContext`c) $CellContext`h\ \[Phi] + ( 2880 (-8 + $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L2^6)) Pi^8, (((((Rational[-1, 113400] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-6)) $CellContext`L2^(-8)) \ ((($CellContext`c^2 (22 + 5 $CellContext`c)) (-61984 + $CellContext`c (-11992 + 215 $CellContext`c))) $CellContext`L1^6 - (((($CellContext`c \ (22 + 5 $CellContext`c)) (-8960 + $CellContext`c (756 + 425 $CellContext`c))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ ((($CellContext`c^2 (22 + 5 $CellContext`c)) ( 608 + $CellContext`c (1224 + 205 $CellContext`c)) - (( 240 $CellContext`c) ( 3520 + $CellContext`c ( 32 + $CellContext`c (1094 + 205 $CellContext`c)))) $CellContext`h\[Phi] + ( 2880 (4224 + $CellContext`c (-4936 + $CellContext`c (234 + 205 $CellContext`c)))) $CellContext`h\[Phi]^2) \ $CellContext`L1^2) $CellContext`L2^4 + (((22 + 5 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 (4 + 5 $CellContext`c) - (( 240 (-4 + $CellContext`c)) $CellContext`c) $CellContext`h\ \[Phi] + ( 2880 (-8 + $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L2^6)) Pi^8}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, {((((Rational[ 1, 4320]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^4, 0, (((( Rational[ 1, 45]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((( Rational[ 1, 30]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((( Rational[ 1, 15]/$CellContext`c) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-(-8 + $CellContext`c)) $CellContext`L1^2 + \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 45360] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`c $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^6, 0, ((((( Rational[-1, 945] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((3 $CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, ((((( Rational[-1, 630] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((3 $CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, (((( Rational[ 1, 315] $CellContext`c^(-2)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((((-3) (-16 + $CellContext`c)) $CellContext`c) \ $CellContext`L1^4 + (((2 (-8 + $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ ($CellContext`c - 24 $CellContext`h\[Phi])^2 $CellContext`L2^4)) Pi^6}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {(((((Rational[1, 65318400] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-8)) $CellContext`L2^(-8)) \ ((((-$CellContext`c^4) (-104 + 5 $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`L1^8 + (((((4 $CellContext`c^3) ( 4 + 5 $CellContext`c)) (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^6) $CellContext`L2^2 - \ ((((6 $CellContext`c^2) (22 + 5 $CellContext`c)) ((5 $CellContext`c^2) ( 8 + $CellContext`c) - ((48 $CellContext`c) (32 + 5 $CellContext`c)) $CellContext`h\[Phi] + ( 192 (76 + 15 $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^4) $CellContext`L2^4 + (((((4 $CellContext`c) (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 (4 + 5 $CellContext`c) - (( 240 (-4 + $CellContext`c)) $CellContext`c) $CellContext`h\ \[Phi] + ( 2880 (-8 + $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^6 + (((-$CellContext`c^4) (-104 + 5 $CellContext`c)) (22 + 5 $CellContext`c) + (((96 $CellContext`c^3) (-128 + 5 $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`h\[Phi] - (( 1152 $CellContext`c^2) (-11096 + (5 $CellContext`c) (-386 + 15 $CellContext`c))) $CellContext`h\[Phi]^2 + (( 276480 $CellContext`c) (-968 + ( 5 (-30 + $CellContext`c)) $CellContext`c)) $CellContext`h\ \[Phi]^3 - ( 1658880 (-1232 + ( 5 (-34 + $CellContext`c)) $CellContext`c)) $CellContext`h\ \[Phi]^4) $CellContext`L2^8)) Pi^8, 0, ((((Rational[-1, 340200] $CellContext`c^(-3)) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c^3 (368 + 55 $CellContext`c)) $CellContext`L1^6 - ((((3 $CellContext`c^2) ( 172 + 35 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ (((9 $CellContext`c) ($CellContext`c^2 (16 + 5 $CellContext`c) + (( 80 (8 - 3 $CellContext`c)) $CellContext`c) $CellContext`h\[Phi] + ( 320 (-68 + 9 $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L1^2) $CellContext`L2^4 + (($CellContext`c - 24 $CellContext`h\[Phi]) ($CellContext`c^2 (4 + 5 $CellContext`c) - (( 240 (-4 + $CellContext`c)) $CellContext`c) \ $CellContext`h\[Phi] + ( 2880 (-8 + $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L2^6)) Pi^8, (((( Rational[-1, 226800] $CellContext`c^(-3)) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c^3 (808 + 155 $CellContext`c)) $CellContext`L1^6 - ((($CellContext`c^2 ( 1396 + 305 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ (($CellContext`c ( 145 $CellContext`c^3 + (8 $CellContext`c^2) (73 - 870 $CellContext`h\[Phi]) - 449280 $CellContext`h\[Phi]^2 + (( 960 $CellContext`c) $CellContext`h\[Phi]) (8 + 87 $CellContext`h\[Phi]))) $CellContext`L1^2) \ $CellContext`L2^4 + (($CellContext`c - 24 $CellContext`h\[Phi]) ($CellContext`c^2 (4 + 5 $CellContext`c) - (( 240 (-4 + $CellContext`c)) $CellContext`c) \ $CellContext`h\[Phi] + ( 2880 (-8 + $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L2^6)) Pi^8, (((((Rational[-1, 113400] $CellContext`c^(-3))/(22 + 5 $CellContext`c)) $CellContext`L1^(-6)) $CellContext`L2^(-8)) \ ((($CellContext`c^2 (22 + 5 $CellContext`c)) (-61984 + $CellContext`c (-11992 + 215 $CellContext`c))) $CellContext`L1^6 - (((($CellContext`c ( 22 + 5 $CellContext`c)) (-8960 + $CellContext`c (756 + 425 $CellContext`c))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 + \ ((($CellContext`c^2 (22 + 5 $CellContext`c)) ( 608 + $CellContext`c (1224 + 205 $CellContext`c)) - (( 240 $CellContext`c) ( 3520 + $CellContext`c ( 32 + $CellContext`c (1094 + 205 $CellContext`c)))) $CellContext`h\[Phi] + ( 2880 (4224 + $CellContext`c (-4936 + $CellContext`c (234 + 205 $CellContext`c)))) $CellContext`h\[Phi]^2) \ $CellContext`L1^2) $CellContext`L2^4 + (((22 + 5 $CellContext`c) ($CellContext`c - 24 $CellContext`h\[Phi])) ($CellContext`c^2 (4 + 5 $CellContext`c) - (( 240 (-4 + $CellContext`c)) $CellContext`c) \ $CellContext`h\[Phi] + ( 2880 (-8 + $CellContext`c)) $CellContext`h\[Phi]^2)) \ $CellContext`L2^6)) Pi^8}, 0, 5, 1]}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.7041154839401503`*^9, 3.7041155058482423`*^9}, 3.7041200391757126`*^9, 3.70412009230025*^9, {3.7041249457334986`*^9, 3.704124946982025*^9}, {3.704126863198118*^9, 3.7041268827047496`*^9}, { 3.7041272877963457`*^9, 3.704127288633995*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["JS(\[Rho]_A(L1,q1),\[Rho]_A(L2,q2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, {3.704116595159308*^9, 3.704116597929334*^9}, {3.7041177049986935`*^9, 3.704117707948104*^9}, 3.704120028560308*^9, {3.704120086479438*^9, 3.7041200867951765`*^9}, 3.7041268511846633`*^9}], Cell[BoxData[ RowBox[{ RowBox[{"JSL1q1L2q2", "=", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"4320", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"30", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{"8", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}], "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "4"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 4320] $CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) ($CellContext`L1^2 - $CellContext`L2^2)^2) Pi^4, 0, (((((Rational[-1, 45] $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^2 + $CellContext`L1^2 \ $CellContext`q2^2), ((((( Rational[-1, 30] $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^3 + $CellContext`L1^2 \ $CellContext`q2^3), (((( Rational[ 1, 15]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) Pi^4) ( 8 ($CellContext`L2^2 $CellContext`q1^2 - $CellContext`L1^2 \ $CellContext`q2^2)^2 + (($CellContext`c ($CellContext`L1 - $CellContext`L2)) \ ($CellContext`L1 + $CellContext`L2)) ($CellContext`L2^2 $CellContext`q1^4 - \ $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "+", SuperscriptBox["L2", "2"]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"45360", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", SuperscriptBox["L2", "4"], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{"3", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["q1", "2"]}], "+", SuperscriptBox["q2", "2"]}], ")"}]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", SuperscriptBox["L2", "4"], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{"3", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["q2", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", SuperscriptBox["q1", "3"]}], "+", SuperscriptBox["q2", "3"]}], ")"}]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"630", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}], ")"}]}]], "+", FractionBox[ RowBox[{ SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"3", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{"32", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "+", SuperscriptBox["L2", "2"]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "3"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"315", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 45360] $CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`L1^2 - $CellContext`L2^2)^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) Pi^6, 0, (((((Rational[-1, 945] $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-3) $CellContext`L2^4) $CellContext`q1^2 + ( 3 $CellContext`L1^4) $CellContext`q2^2 + ($CellContext`L1^2 \ $CellContext`L2^2) (-$CellContext`q1^2 + $CellContext`q2^2)), ((((( Rational[-1, 630] $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-3) $CellContext`L2^4) $CellContext`q1^3 + ( 3 $CellContext`L1^4) $CellContext`q2^3 + ($CellContext`L1^2 \ $CellContext`L2^2) (-$CellContext`q1^3 + $CellContext`q2^3)), (((( Rational[ 1, 315]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) Pi^6) (($CellContext`L2^2 ($CellContext`c $CellContext`L1^4 + (( 2 (-8 + $CellContext`c)) $CellContext`L1^2) \ $CellContext`L2^2 - ( 3 (-16 + $CellContext`c)) $CellContext`L2^4)) \ $CellContext`q1^4 - (((( 32 $CellContext`L1^2) $CellContext`L2^2) ($CellContext`L1^2 + \ $CellContext`L2^2)) $CellContext`q1^2) $CellContext`q2^2 + ($CellContext`L1^2 \ (((-3) (-16 + $CellContext`c)) $CellContext`L1^4 + (( 2 (-8 + $CellContext`c)) $CellContext`L1^2) \ $CellContext`L2^2 + $CellContext`c $CellContext`L2^4)) $CellContext`q2^4)}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "104"}], "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"2", " ", RowBox[{"(", RowBox[{"112", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "104"}], "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"65318400", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]]}], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"368", "+", RowBox[{"55", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"368", "+", RowBox[{"55", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", RowBox[{"(", RowBox[{"74", "+", RowBox[{"25", " ", "c"}]}], ")"}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"74", "+", RowBox[{"25", " ", "c"}]}], ")"}], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"340200", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"808", "+", RowBox[{"155", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "3"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"808", "+", RowBox[{"155", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "6"}], " ", RowBox[{"(", RowBox[{"98", "+", RowBox[{"25", " ", "c"}]}], ")"}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{"6", " ", RowBox[{"(", RowBox[{"98", "+", RowBox[{"25", " ", "c"}]}], ")"}], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"226800", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"113400", " ", "c", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"608", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"1224", "+", RowBox[{"205", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"8960", "-", RowBox[{"c", " ", RowBox[{"(", RowBox[{"756", "+", RowBox[{"425", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "61984"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "11992"}], "+", RowBox[{"215", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{"48", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"172", "+", RowBox[{"35", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"10", " ", RowBox[{"(", RowBox[{"184", "+", RowBox[{"41", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"172", "+", RowBox[{"35", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "61984"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "11992"}], "+", RowBox[{"215", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"8960", "-", RowBox[{"c", " ", RowBox[{"(", RowBox[{"756", "+", RowBox[{"425", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"608", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"1224", "+", RowBox[{"205", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"4", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((( Rational[-1, 65318400] $CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) ($CellContext`L1^2 - $CellContext`L2^2)^2) ((-104 + 5 $CellContext`c) $CellContext`L1^4 - (( 2 (112 + 5 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + \ (-104 + 5 $CellContext`c) $CellContext`L2^4)) Pi^8, 0, (((((Rational[ 1, 340200] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) (((368 + 55 $CellContext`c) $CellContext`L2^6) $CellContext`q1^2 - ((368 + 55 $CellContext`c) $CellContext`L1^6) $CellContext`q2^2 + \ ($CellContext`L1^2 $CellContext`L2^4) (((-2) (74 + 25 $CellContext`c)) $CellContext`q1^2 + (4 + 5 $CellContext`c) $CellContext`q2^2) + ($CellContext`L1^4 \ $CellContext`L2^2) ((-(4 + 5 $CellContext`c)) $CellContext`q1^2 + ( 2 (74 + 25 $CellContext`c)) $CellContext`q2^2)), ((((( Rational[ 1, 226800] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) (((808 + 155 $CellContext`c) $CellContext`L2^6) $CellContext`q1^3 - (( 808 + 155 $CellContext`c) $CellContext`L1^6) $CellContext`q2^3 + \ ($CellContext`L1^2 $CellContext`L2^4) (((-6) (98 + 25 $CellContext`c)) $CellContext`q1^3 + (4 + 5 $CellContext`c) $CellContext`q2^3) + ($CellContext`L1^4 \ $CellContext`L2^2) ((-(4 + 5 $CellContext`c)) $CellContext`q1^3 + ( 6 (98 + 25 $CellContext`c)) $CellContext`q2^3)), (((( Rational[ 1, 113400]/$CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) Pi^8) (((-$CellContext`L2^2) (($CellContext`c (4 + 5 $CellContext`c)) $CellContext`L1^6 + (( 608 + $CellContext`c (1224 + 205 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^2 + \ ((8960 - $CellContext`c (756 + 425 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^4 + \ (-61984 + $CellContext`c (-11992 + 215 $CellContext`c)) $CellContext`L2^6)) $CellContext`q1^4 - \ ((((48 $CellContext`L1^2) $CellContext`L2^2) ((172 + 35 $CellContext`c) $CellContext`L1^4 + (( 10 (184 + 41 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + ( 172 + 35 $CellContext`c) $CellContext`L2^4)) \ $CellContext`q1^2) $CellContext`q2^2 - ($CellContext`L1^2 ((-61984 + \ $CellContext`c (-11992 + 215 $CellContext`c)) $CellContext`L1^6 + (( 8960 - $CellContext`c (756 + 425 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^2 + \ ((608 + $CellContext`c (1224 + 205 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^4 + \ ($CellContext`c (4 + 5 $CellContext`c)) $CellContext`L2^6)) $CellContext`q2^4)}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, {((((Rational[ 1, 4320] $CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) ($CellContext`L1^2 - $CellContext`L2^2)^2) Pi^4, 0, (((((Rational[-1, 45] $CellContext`L1^(-4)) ($CellContext`L1 - $CellContext`L2)) \ $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^2 + $CellContext`L1^2 \ $CellContext`q2^2), ((((( Rational[-1, 30] $CellContext`L1^(-4)) ($CellContext`L1 - $CellContext`L2)) \ $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^3 + $CellContext`L1^2 \ $CellContext`q2^3), (((( Rational[ 1, 15]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) Pi^4) ( 8 ($CellContext`L2^2 $CellContext`q1^2 - $CellContext`L1^2 \ $CellContext`q2^2)^2 + (($CellContext`c ($CellContext`L1 - $CellContext`L2)) \ ($CellContext`L1 + $CellContext`L2)) ($CellContext`L2^2 $CellContext`q1^4 - \ $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((( Rational[ 1, 45360] $CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`L1^2 - $CellContext`L2^2)^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) Pi^6, 0, (((((Rational[-1, 945] $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-3) $CellContext`L2^4) $CellContext`q1^2 + ( 3 $CellContext`L1^4) $CellContext`q2^2 + ($CellContext`L1^2 \ $CellContext`L2^2) (-$CellContext`q1^2 + $CellContext`q2^2)), ((((( Rational[-1, 630] $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-3) $CellContext`L2^4) $CellContext`q1^3 + ( 3 $CellContext`L1^4) $CellContext`q2^3 + ($CellContext`L1^2 \ $CellContext`L2^2) (-$CellContext`q1^3 + $CellContext`q2^3)), (((( Rational[ 1, 315]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) Pi^6) (($CellContext`L2^2 ($CellContext`c $CellContext`L1^4 + (( 2 (-8 + $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 - \ (3 (-16 + $CellContext`c)) $CellContext`L2^4)) $CellContext`q1^4 - (((( 32 $CellContext`L1^2) $CellContext`L2^2) ($CellContext`L1^2 + \ $CellContext`L2^2)) $CellContext`q1^2) $CellContext`q2^2 + ($CellContext`L1^2 \ (((-3) (-16 + $CellContext`c)) $CellContext`L1^4 + (( 2 (-8 + $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + \ $CellContext`c $CellContext`L2^4)) $CellContext`q2^4)}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((( Rational[-1, 65318400] $CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) ($CellContext`L1^2 - $CellContext`L2^2)^2) ((-104 + 5 $CellContext`c) $CellContext`L1^4 - (( 2 (112 + 5 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + (-104 + 5 $CellContext`c) $CellContext`L2^4)) Pi^8, 0, (((((Rational[ 1, 340200] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) (((368 + 55 $CellContext`c) $CellContext`L2^6) $CellContext`q1^2 - ((368 + 55 $CellContext`c) $CellContext`L1^6) $CellContext`q2^2 + \ ($CellContext`L1^2 $CellContext`L2^4) (((-2) (74 + 25 $CellContext`c)) $CellContext`q1^2 + (4 + 5 $CellContext`c) $CellContext`q2^2) + ($CellContext`L1^4 \ $CellContext`L2^2) ((-(4 + 5 $CellContext`c)) $CellContext`q1^2 + ( 2 (74 + 25 $CellContext`c)) $CellContext`q2^2)), ((((( Rational[ 1, 226800] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) (((808 + 155 $CellContext`c) $CellContext`L2^6) $CellContext`q1^3 - ((808 + 155 $CellContext`c) $CellContext`L1^6) $CellContext`q2^3 + \ ($CellContext`L1^2 $CellContext`L2^4) (((-6) (98 + 25 $CellContext`c)) $CellContext`q1^3 + (4 + 5 $CellContext`c) $CellContext`q2^3) + ($CellContext`L1^4 \ $CellContext`L2^2) ((-(4 + 5 $CellContext`c)) $CellContext`q1^3 + ( 6 (98 + 25 $CellContext`c)) $CellContext`q2^3)), (((( Rational[ 1, 113400]/$CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) Pi^8) (((-$CellContext`L2^2) (($CellContext`c (4 + 5 $CellContext`c)) $CellContext`L1^6 + (( 608 + $CellContext`c (1224 + 205 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^2 + \ ((8960 - $CellContext`c (756 + 425 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^4 + \ (-61984 + $CellContext`c (-11992 + 215 $CellContext`c)) $CellContext`L2^6)) $CellContext`q1^4 - \ ((((48 $CellContext`L1^2) $CellContext`L2^2) ((172 + 35 $CellContext`c) $CellContext`L1^4 + (( 10 (184 + 41 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + ( 172 + 35 $CellContext`c) $CellContext`L2^4)) $CellContext`q1^2) \ $CellContext`q2^2 - ($CellContext`L1^2 ((-61984 + $CellContext`c (-11992 + 215 $CellContext`c)) $CellContext`L1^6 + (( 8960 - $CellContext`c (756 + 425 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^2 + (( 608 + $CellContext`c (1224 + 205 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^4 + \ ($CellContext`c (4 + 5 $CellContext`c)) $CellContext`L2^6)) $CellContext`q2^4)}, 0, 5, 1]}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.7041177096676693`*^9, 3.704117722947776*^9}, 3.7041200520732484`*^9, 3.7041200892496595`*^9, {3.7041256489764595`*^9, 3.7041256504155164`*^9}, {3.7041268672817106`*^9, 3.704126883505083*^9}, { 3.7041279326025686`*^9, 3.7041279339044714`*^9}}] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Section 3.3 Schatten 2-norm", "Section", CellChangeTimes->{{3.7039542022131257`*^9, 3.703954219345484*^9}, { 3.7039553305656457`*^9, 3.703955332918915*^9}, {3.704042560801203*^9, 3.704042566640339*^9}, {3.704120014430778*^9, 3.704120020367242*^9}, { 3.704120063669981*^9, 3.7041200710617695`*^9}, 3.7041202585198755`*^9, { 3.704126824559267*^9, 3.704126842406231*^9}, 3.7041293515724216`*^9, { 3.704129387492532*^9, 3.7041293906268845`*^9}, 3.70417290264989*^9, { 3.7118130820662737`*^9, 3.7118130962984133`*^9}, {3.7119065130847445`*^9, 3.7119065141198783`*^9}}], Cell[CellGroupData[{ Cell["||\[Rho]_A(L1,\[Phi]1)-\[Rho]_A(L2,\[Phi]2)||_2^2", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, 3.704120023776886*^9, {3.704120076714172*^9, 3.704120078900853*^9}, { 3.704126845060828*^9, 3.7041268452944665`*^9}, {3.704129395817523*^9, 3.7041294274234285`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"L1\[Phi]1L2\[Phi]222", "=", RowBox[{ SuperscriptBox["\[ScriptL]", RowBox[{ RowBox[{"-", "c"}], "/", "8"}]], RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["\[ScriptL]", "4"]}], RowBox[{"9216", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]2"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]2", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "+", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]1"}], "-", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]1", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["\[ScriptL]", "6"]}], RowBox[{"4423680", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"178362777600", " ", "c"}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ FractionBox["1", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}]], RowBox[{"700", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"68", "+", RowBox[{"7", " ", "c"}]}], ")"}]}], "-", RowBox[{"72", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "248"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"938", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"617", "+", RowBox[{"70", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", "h\[Phi]1"}], "+", RowBox[{"1728", " ", RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]1", "2"]}], "-", RowBox[{"13824", " ", RowBox[{"(", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]1", "3"]}]}], SuperscriptBox["L1", "6"]], "+", FractionBox[ RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"68", "+", RowBox[{"7", " ", "c"}]}], ")"}]}], "+", RowBox[{"72", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "248"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"938", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"617", "+", RowBox[{"70", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", "h\[Phi]2"}], "-", RowBox[{"1728", " ", RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]2", "2"]}], "+", RowBox[{"13824", " ", RowBox[{"(", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]2", "3"]}]}], SuperscriptBox["L2", "6"]]}], ")"}], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], SuperscriptBox["L1", "2"]], "-", FractionBox[ RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], SuperscriptBox["L2", "2"]]}], ")"}]}]}], "+", FractionBox[ RowBox[{"21", " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]2"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]2", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "+", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]1"}], "-", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]1", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], "2"]}], RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", FractionBox[ RowBox[{"960", " ", RowBox[{"(", RowBox[{"416", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"275", "+", RowBox[{"56", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"31", " ", "c", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], "-", SuperscriptBox["L2", "6"]}], ")"}]}], "+", RowBox[{"504", " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "h\[Phi]2"}], " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{"h\[Phi]1", " ", SuperscriptBox["L2", "6"]}]}], ")"}]}]}], ")"}]}], RowBox[{ RowBox[{"(", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["\[ScriptL]", "8"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, {(((((Rational[1, 9216]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-4)) $CellContext`L2^(-4)) \ (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)^2) Pi^4, 0, ((((((Rational[1, 4423680]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)) (($CellContext`c ( 22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi]2 + 2880 $CellContext`h\[Phi]2^2) $CellContext`L1^4 + \ ((-$CellContext`c) (22 + 5 $CellContext`c) + ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi]1 - 2880 $CellContext`h\[Phi]1^2) $CellContext`L2^4)) Pi^6, 0, ((Rational[ 1, 178362777600]/$CellContext`c) ((((700 (6 + $CellContext`c))/(29 + 70 $CellContext`c)) (((($CellContext`c (-1 + 2 $CellContext`c)) ( 22 + 5 $CellContext`c)) (68 + 7 $CellContext`c) - ( 72 (-248 + $CellContext`c ( 938 + $CellContext`c (617 + 70 $CellContext`c)))) $CellContext`h\[Phi]1 + (( 1728 (4 + $CellContext`c)) (29 + 70 $CellContext`c)) $CellContext`h\[Phi]1^2 - ( 13824 (29 + 70 $CellContext`c)) $CellContext`h\[Phi]1^3) \ $CellContext`L1^(-6) + ((((-$CellContext`c) (-1 + 2 $CellContext`c)) (22 + 5 $CellContext`c)) (68 + 7 $CellContext`c) + ( 72 (-248 + $CellContext`c ( 938 + $CellContext`c (617 + 70 $CellContext`c)))) $CellContext`h\[Phi]2 - (( 1728 (4 + $CellContext`c)) (29 + 70 $CellContext`c)) $CellContext`h\[Phi]2^2 + ( 13824 (29 + 70 $CellContext`c)) $CellContext`h\[Phi]2^3) \ $CellContext`L2^(-6))) (($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L1^(-2) - \ ($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L2^(-2)) + ((((21/(22 + 5 $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) (($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi]2 + 2880 $CellContext`h\[Phi]2^2) $CellContext`L1^4 + \ ((-$CellContext`c) (22 + 5 $CellContext`c) + ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi]1 - 2880 $CellContext`h\[Phi]1^2) $CellContext`L2^4)^2 + (((((960/( 29 + 70 $CellContext`c)) ( 416 + $CellContext`c (275 + 56 $CellContext`c))) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) (($CellContext`c - 24 $CellContext`h\[Phi]2) $CellContext`L1^2 - ($CellContext`c - 24 $CellContext`h\[Phi]1) $CellContext`L2^2)) (( 31 $CellContext`c) ($CellContext`L1^6 - $CellContext`L2^6) + 504 ((-$CellContext`h\[Phi]2) $CellContext`L1^6 + $CellContext`h\ \[Phi]1 $CellContext`L2^6)))) Pi^8}, 4, 10, 1], Editable->False], ")"}]}]}], ";"}]], "Input", CellChangeTimes->{{3.704042631409958*^9, 3.704042659643123*^9}, 3.7041200337358904`*^9, 3.7041200746500072`*^9, {3.704124558584817*^9, 3.7041245601233606`*^9}, {3.704126857355027*^9, 3.7041269027230988`*^9}, 3.7041293580461025`*^9, {3.7041294329946194`*^9, 3.7041294402358403`*^9}, { 3.704129646021199*^9, 3.7041296545703964`*^9}, 3.704129947084055*^9, 3.704130404639619*^9}] }, Closed]], Cell[CellGroupData[{ Cell["||\[Rho]_A(L1,\[Phi]),\[Rho]_A(L2,q)||_2^2", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, 3.7041200258581767`*^9, { 3.7041200815416093`*^9, 3.7041200819048214`*^9}, 3.704126849767155*^9, { 3.7041294033741727`*^9, 3.7041294213640456`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"L1\[Phi]L2q22", "=", RowBox[{ SuperscriptBox["\[ScriptL]", RowBox[{ RowBox[{"-", "c"}], "/", "8"}]], RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"9216", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "2"]}], RowBox[{"96", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "3"]}], RowBox[{"64", " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"32", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((((Rational[1, 9216]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^4, 0, (((((Rational[1, 96]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((((Rational[1, 64]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((((Rational[-1, 32]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-8 + $CellContext`c) $CellContext`L1^2 - \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "+", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "-", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"4423680", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"9", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"10", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "2"]}], RowBox[{"92160", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"29", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"30", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "3"]}], RowBox[{"61440", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "3520"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"438", "+", RowBox[{"205", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"210", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "4"]}], RowBox[{"30720", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "6"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((((Rational[1, 4423680]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L1^4 + ((-$CellContext`c) ( 22 + 5 $CellContext`c) + ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] - 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, 0, (((((Rational[1, 92160]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (((9 $CellContext`c) (22 + 5 $CellContext`c)) $CellContext`L1^4 - ((( 10 (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) \ $CellContext`L2^2 + ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)) Pi^6, (((((Rational[1, 61440]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (((29 $CellContext`c) (22 + 5 $CellContext`c)) $CellContext`L1^4 - ((( 30 (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) \ $CellContext`L2^2 + ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)) Pi^6, (((((Rational[1, 30720]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((-3520 + $CellContext`c (438 + 205 $CellContext`c)) $CellContext`L1^4 - ((( 210 (6 + $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) \ $CellContext`L2^2 + ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)) Pi^6}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{ FractionBox["1", RowBox[{"178362777600", " ", "c"}]], RowBox[{ RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"700", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"68", "+", RowBox[{"7", " ", "c"}]}], ")"}]}], "-", RowBox[{"72", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "248"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"938", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"617", "+", RowBox[{"70", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"1728", " ", RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "-", RowBox[{"13824", " ", RowBox[{"(", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}]}], SuperscriptBox["L1", "6"]], "-", FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"68", "+", RowBox[{"7", " ", "c"}]}], ")"}]}], SuperscriptBox["L2", "6"]]}], ")"}], " ", RowBox[{"(", RowBox[{ FractionBox[ RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], SuperscriptBox["L1", "2"]], "-", FractionBox["c", SuperscriptBox["L2", "2"]]}], ")"}]}], RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}]], "+", FractionBox[ RowBox[{"21", " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "+", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "-", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], "2"]}], RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", FractionBox[ RowBox[{"960", " ", RowBox[{"(", RowBox[{"416", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"275", "+", RowBox[{"56", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"504", " ", "h\[Phi]", " ", SuperscriptBox["L2", "6"]}], "+", RowBox[{"31", " ", "c", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], "-", SuperscriptBox["L2", "6"]}], ")"}]}]}], ")"}]}], RowBox[{ RowBox[{"(", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}]}], "+", RowBox[{ FractionBox["1", RowBox[{"185794560", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "282672"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "263236"}], "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "9492"}], "+", RowBox[{"235", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"21", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "17712"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14740"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "3552"}], "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"21", " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"10512", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"5020", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"96", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"504", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"60480", " ", RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "-", RowBox[{"483840", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "2"]}]}], "+", RowBox[{ FractionBox["1", RowBox[{"123863040", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "3046608"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2235388"}], "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "70332"}], "+", RowBox[{"685", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"21", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "158832"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "113540"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "24672"}], "+", RowBox[{"155", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"63", " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"10512", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"5020", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"96", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"504", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"60480", " ", RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "-", RowBox[{"483840", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "3"]}]}], "+", RowBox[{ FractionBox["1", RowBox[{"61931520", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"13934592", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1598448"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "4469620"}], "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "172236"}], "+", RowBox[{"955", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"21", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "534192"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "315380"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "60432"}], "+", RowBox[{"215", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"441", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"240", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"2880", " ", SuperscriptBox["h\[Phi]", "2"]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"10512", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"5020", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"96", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}]}], "-", RowBox[{"504", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"60480", " ", RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "-", RowBox[{"483840", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((Rational[ 1, 178362777600]/$CellContext`c) (((( 700 (6 + $CellContext`c))/(29 + 70 $CellContext`c)) (((($CellContext`c (-1 + 2 $CellContext`c)) (22 + 5 $CellContext`c)) (68 + 7 $CellContext`c) - ( 72 (-248 + $CellContext`c ( 938 + $CellContext`c (617 + 70 $CellContext`c)))) $CellContext`h\[Phi] + (( 1728 (4 + $CellContext`c)) (29 + 70 $CellContext`c)) $CellContext`h\[Phi]^2 - ( 13824 (29 + 70 $CellContext`c)) $CellContext`h\[Phi]^3) \ $CellContext`L1^(-6) - ((($CellContext`c (-1 + 2 $CellContext`c)) (22 + 5 $CellContext`c)) (68 + 7 $CellContext`c)) $CellContext`L2^(-6))) (($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^(-2) - \ $CellContext`c $CellContext`L2^(-2)) + ((((21/(22 + 5 $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) (($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L1^4 + ((-$CellContext`c) \ (22 + 5 $CellContext`c) + (240 (2 + $CellContext`c)) $CellContext`h\[Phi] - 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)^2 + ((((( 960/(29 + 70 $CellContext`c)) ( 416 + $CellContext`c (275 + 56 $CellContext`c))) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + \ ($CellContext`c ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + \ $CellContext`L2))) ((504 $CellContext`h\[Phi]) $CellContext`L2^6 + ( 31 $CellContext`c) ($CellContext`L1^6 - \ $CellContext`L2^6)))) Pi^8, 0, ((((Rational[ 1, 185794560]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c (-282672 + $CellContext`c (-263236 + ( 7 $CellContext`c) (-9492 + 235 $CellContext`c)))) $CellContext`L1^6 - ((( 21 (-17712 + $CellContext`c (-14740 + $CellContext`c (-3552 + 55 $CellContext`c)))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) \ $CellContext`L2^2 - ((( 21 (216 + $CellContext`c (62 + 5 $CellContext`c))) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ($CellContext`c ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) - (( 504 (2 + $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) $CellContext`h\[Phi] + (( 60480 (4 + $CellContext`c)) ( 6 + $CellContext`c)) $CellContext`h\[Phi]^2 - ( 483840 ( 6 + $CellContext`c)) $CellContext`h\[Phi]^3) \ $CellContext`L2^6)) Pi^8, (((( Rational[ 1, 123863040]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c (-3046608 + $CellContext`c (-2235388 + \ (7 $CellContext`c) (-70332 + 685 $CellContext`c)))) $CellContext`L1^6 - ((( 21 (-158832 + $CellContext`c (-113540 + $CellContext`c \ (-24672 + 155 $CellContext`c)))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) \ $CellContext`L2^2 - ((( 63 (216 + $CellContext`c (62 + 5 $CellContext`c))) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ($CellContext`c ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) - (( 504 (2 + $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) $CellContext`h\[Phi] + (( 60480 (4 + $CellContext`c)) ( 6 + $CellContext`c)) $CellContext`h\[Phi]^2 - ( 483840 ( 6 + $CellContext`c)) $CellContext`h\[Phi]^3) \ $CellContext`L2^6)) Pi^8, (((((Rational[1, 61931520]/$CellContext`c)/(22 + 5 $CellContext`c)) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (((22 + 5 $CellContext`c) ( 13934592 + $CellContext`c (-1598448 + $CellContext`c \ (-4469620 + (7 $CellContext`c) (-172236 + 955 $CellContext`c))))) $CellContext`L1^6 - (((( 21 (22 + 5 $CellContext`c)) (-534192 + $CellContext`c (-315380 + \ $CellContext`c (-60432 + 215 $CellContext`c)))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) \ $CellContext`L2^2 - ((((441 (6 + $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ((22 + 5 $CellContext`c) ($CellContext`c ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) - (( 504 (2 + $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) $CellContext`h\[Phi] + (( 60480 (4 + $CellContext`c)) ( 6 + $CellContext`c)) $CellContext`h\[Phi]^2 - ( 483840 ( 6 + $CellContext`c)) $CellContext`h\[Phi]^3)) \ $CellContext`L2^6)) Pi^8}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, {(((((Rational[1, 9216]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^4, 0, (((((Rational[1, 96]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((((Rational[1, 64]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-$CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4, (((((Rational[-1, 32]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-2)) \ $CellContext`L2^(-4)) ((-8 + $CellContext`c) $CellContext`L1^2 - \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) Pi^4}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((((Rational[1, 4423680]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) (($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L1^4 + ((-$CellContext`c) (22 + 5 $CellContext`c) + ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] - 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) Pi^6, 0, (((((Rational[1, 92160]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (((9 $CellContext`c) (22 + 5 $CellContext`c)) $CellContext`L1^4 - ((( 10 (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)) Pi^6, (((((Rational[1, 61440]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) (((29 $CellContext`c) (22 + 5 $CellContext`c)) $CellContext`L1^4 - ((( 30 (22 + 5 $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)) Pi^6, (((((Rational[1, 30720]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-6)) ((-3520 + $CellContext`c (438 + 205 $CellContext`c)) $CellContext`L1^4 - ((( 210 (6 + $CellContext`c)) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^2) $CellContext`L2^2 + \ ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)) Pi^6}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((Rational[ 1, 178362777600]/$CellContext`c) ((((700 (6 + $CellContext`c))/( 29 + 70 $CellContext`c)) (((($CellContext`c (-1 + 2 $CellContext`c)) (22 + 5 $CellContext`c)) (68 + 7 $CellContext`c) - ( 72 (-248 + $CellContext`c ( 938 + $CellContext`c (617 + 70 $CellContext`c)))) $CellContext`h\[Phi] + (( 1728 (4 + $CellContext`c)) (29 + 70 $CellContext`c)) $CellContext`h\[Phi]^2 - ( 13824 (29 + 70 $CellContext`c)) $CellContext`h\[Phi]^3) \ $CellContext`L1^(-6) - ((($CellContext`c (-1 + 2 $CellContext`c)) (22 + 5 $CellContext`c)) (68 + 7 $CellContext`c)) $CellContext`L2^(-6))) (($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L1^(-2) - \ $CellContext`c $CellContext`L2^(-2)) + ((((21/(22 + 5 $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) (($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L1^4 + ((-$CellContext`c) ( 22 + 5 $CellContext`c) + ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] - 2880 $CellContext`h\[Phi]^2) $CellContext`L2^4)^2 + ((((( 960/(29 + 70 $CellContext`c)) ( 416 + $CellContext`c (275 + 56 $CellContext`c))) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))) (( 504 $CellContext`h\[Phi]) $CellContext`L2^6 + ( 31 $CellContext`c) ($CellContext`L1^6 - $CellContext`L2^6)))) Pi^8, 0, (((( Rational[ 1, 185794560]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c (-282672 + $CellContext`c (-263236 + ( 7 $CellContext`c) (-9492 + 235 $CellContext`c)))) $CellContext`L1^6 - ((( 21 (-17712 + $CellContext`c (-14740 + $CellContext`c (-3552 + 55 $CellContext`c)))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 - \ (((21 (216 + $CellContext`c (62 + 5 $CellContext`c))) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ($CellContext`c ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) - (( 504 (2 + $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) $CellContext`h\[Phi] + (( 60480 (4 + $CellContext`c)) ( 6 + $CellContext`c)) $CellContext`h\[Phi]^2 - ( 483840 ( 6 + $CellContext`c)) $CellContext`h\[Phi]^3) \ $CellContext`L2^6)) Pi^8, (((( Rational[ 1, 123863040]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (($CellContext`c (-3046608 + $CellContext`c (-2235388 + \ (7 $CellContext`c) (-70332 + 685 $CellContext`c)))) $CellContext`L1^6 - ((( 21 (-158832 + $CellContext`c (-113540 + $CellContext`c (-24672 + 155 $CellContext`c)))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 - \ (((63 (216 + $CellContext`c (62 + 5 $CellContext`c))) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ($CellContext`c ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) - (( 504 (2 + $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) $CellContext`h\[Phi] + (( 60480 (4 + $CellContext`c)) ( 6 + $CellContext`c)) $CellContext`h\[Phi]^2 - ( 483840 ( 6 + $CellContext`c)) $CellContext`h\[Phi]^3) \ $CellContext`L2^6)) Pi^8, (((((Rational[1, 61931520]/$CellContext`c)/(22 + 5 $CellContext`c)) $CellContext`L1^(-6)) $CellContext`L2^(-8)) \ (((22 + 5 $CellContext`c) ( 13934592 + $CellContext`c (-1598448 + $CellContext`c (-4469620 + \ (7 $CellContext`c) (-172236 + 955 $CellContext`c))))) $CellContext`L1^6 - (((( 21 (22 + 5 $CellContext`c)) (-534192 + $CellContext`c (-315380 + \ $CellContext`c (-60432 + 215 $CellContext`c)))) ($CellContext`c - 24 $CellContext`h\[Phi])) $CellContext`L1^4) $CellContext`L2^2 - \ ((((441 (6 + $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) ($CellContext`c (22 + 5 $CellContext`c) - ( 240 (2 + $CellContext`c)) $CellContext`h\[Phi] + 2880 $CellContext`h\[Phi]^2)) $CellContext`L1^2) \ $CellContext`L2^4 + ((22 + 5 $CellContext`c) ($CellContext`c ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) - (( 504 (2 + $CellContext`c)) ( 216 + $CellContext`c (62 + 5 $CellContext`c))) $CellContext`h\[Phi] + (( 60480 (4 + $CellContext`c)) ( 6 + $CellContext`c)) $CellContext`h\[Phi]^2 - ( 483840 ( 6 + $CellContext`c)) $CellContext`h\[Phi]^3)) \ $CellContext`L2^6)) Pi^8}, 0, 5, 1]}, 4, 10, 1], Editable->False], ")"}]}]}], ";"}]], "Input", CellChangeTimes->{{3.7041154839401503`*^9, 3.7041155058482423`*^9}, 3.7041200391757126`*^9, 3.70412009230025*^9, {3.7041249457334986`*^9, 3.704124946982025*^9}, {3.704126863198118*^9, 3.7041268827047496`*^9}, { 3.7041272877963457`*^9, 3.704127288633995*^9}, 3.7041293622530575`*^9, { 3.704129434731191*^9, 3.7041294420370455`*^9}, 3.7041294723161182`*^9, 3.7041296584564953`*^9, {3.704130405487289*^9, 3.704130412631193*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["||\[Rho]_A(L1,q1)-\[Rho]_A(L2,q2)||_2^2", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, {3.704116595159308*^9, 3.704116597929334*^9}, {3.7041177049986935`*^9, 3.704117707948104*^9}, 3.704120028560308*^9, {3.704120086479438*^9, 3.7041200867951765`*^9}, 3.7041268511846633`*^9, {3.704129409635429*^9, 3.7041294298594017`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"L1q1L2q222", "=", RowBox[{ SuperscriptBox["\[ScriptL]", RowBox[{ RowBox[{"-", "c"}], "/", "8"}]], RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"9216", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"96", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"64", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "8"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}], "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "4"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "4"]}]}], ")"}]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"32", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((((Rational[1, 9216] $CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) ($CellContext`L1^2 - $CellContext`L2^2)^2) Pi^4, 0, (((((( Rational[-1, 96] ( 2 + $CellContext`c)) $CellContext`L1^(-4)) \ ($CellContext`L1 - $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + \ $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^2 + \ $CellContext`L1^2 $CellContext`q2^2), (((((( Rational[-1, 64] ( 2 + $CellContext`c)) $CellContext`L1^(-4)) \ ($CellContext`L1 - $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + \ $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^3 + \ $CellContext`L1^2 $CellContext`q2^3), (((((Rational[-1, 32]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) Pi^4) ((-8) ($CellContext`L2^2 $CellContext`q1^2 - \ $CellContext`L1^2 $CellContext`q2^2)^2 + (($CellContext`c ($CellContext`L1 - \ $CellContext`L2)) ($CellContext`L1 + $CellContext`L2)) ((-$CellContext`L2^2) \ $CellContext`q1^4 + $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "+", SuperscriptBox["L2", "2"]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"4423680", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "9"}], " ", SuperscriptBox["L2", "4"], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{"9", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{"q1", "-", "q2"}], ")"}], " ", RowBox[{"(", RowBox[{"q1", "+", "q2"}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"92160", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "29"}], " ", SuperscriptBox["L2", "4"], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{"29", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["q2", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["q1", "3"], "-", SuperscriptBox["q2", "3"]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"61440", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", RowBox[{ FractionBox["1", RowBox[{"30720", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], RowBox[{ RowBox[{"(", RowBox[{"4", "+", "c"}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"210", " ", "c", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "3520"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"438", "+", RowBox[{"205", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "+", RowBox[{"160", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "+", SuperscriptBox["L2", "2"]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "3520"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"438", "+", RowBox[{"205", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"210", " ", "c", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((((((Rational[1, 4423680] $CellContext`c) ( 4 + $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`L1^2 - $CellContext`L2^2)^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) Pi^6, 0, (((((((Rational[1, 92160] (4 + $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-9) $CellContext`L2^4) $CellContext`q1^2 + ( 9 $CellContext`L1^4) $CellContext`q2^2 + (($CellContext`L1^2 \ $CellContext`L2^2) ($CellContext`q1 - $CellContext`q2)) ($CellContext`q1 + \ $CellContext`q2)), (((((((Rational[1, 61440] (4 + $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-29) $CellContext`L2^4) $CellContext`q1^3 + ( 29 $CellContext`L1^4) $CellContext`q2^3 + ($CellContext`L1^2 \ $CellContext`L2^2) ($CellContext`q1^3 - $CellContext`q2^3)), ((((( Rational[1, 30720]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) Pi^6) (($CellContext`L2^2 (($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L1^4 - ((( 210 $CellContext`c) ( 6 + $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + \ (-3520 + $CellContext`c (438 + 205 $CellContext`c)) $CellContext`L2^4)) \ $CellContext`q1^4 + ((((( 160 (22 + 5 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) $CellContext`q1^2) $CellContext`q2^2 + \ ($CellContext`L1^2 ((-3520 + $CellContext`c (438 + 205 $CellContext`c)) $CellContext`L1^4 - ((( 210 $CellContext`c) ( 6 + $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + \ ($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L2^4)) $CellContext`q2^4)}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ RowBox[{ FractionBox["1", RowBox[{"178362777600", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"310032", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"151724", "+", RowBox[{"35", " ", "c", " ", RowBox[{"(", RowBox[{"636", "+", RowBox[{"35", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"18", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"11384", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"354", "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"310032", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"151724", "+", RowBox[{"35", " ", "c", " ", RowBox[{"(", RowBox[{"636", "+", RowBox[{"35", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}]}], "+", RowBox[{ FractionBox["1", RowBox[{"185794560", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"282672", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"263236", "+", RowBox[{"7", " ", RowBox[{"(", RowBox[{"9492", "-", RowBox[{"235", " ", "c"}]}], ")"}], " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "282672"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "263236"}], "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "9492"}], "+", RowBox[{"235", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"10512", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"5020", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"96", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{"2", " ", RowBox[{"(", RowBox[{"36", "+", RowBox[{"7", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"1240", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"402", "+", RowBox[{"35", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "2"}], " ", RowBox[{"(", RowBox[{"36", "+", RowBox[{"7", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"1240", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"402", "+", RowBox[{"35", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"10512", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"5020", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"96", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "2"]}]}], "+", RowBox[{ FractionBox["1", RowBox[{"123863040", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"3046608", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"2235388", "+", RowBox[{"7", " ", RowBox[{"(", RowBox[{"70332", "-", RowBox[{"685", " ", "c"}]}], ")"}], " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "6"], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "3046608"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "2235388"}], "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "70332"}], "+", RowBox[{"685", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["q2", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "4"}], " ", RowBox[{"(", RowBox[{"72216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"37238", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"921", "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q1", "3"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"10512", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"5020", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"96", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"10512", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"5020", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"96", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{"4", " ", RowBox[{"(", RowBox[{"72216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"37238", "+", RowBox[{"7", " ", "c", " ", RowBox[{"(", RowBox[{"921", "+", RowBox[{"55", " ", "c"}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["q", "3"]}]}], "+", RowBox[{ FractionBox["1", RowBox[{"61931520", " ", "c", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], RowBox[{ SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{"21", " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "21"}], " ", "c", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["L1", "4"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"1760", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"526", "+", RowBox[{"21", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "-", RowBox[{"160", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "4"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"1760", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"526", "+", RowBox[{"21", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{"21", " ", "c", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}]}], "-", RowBox[{ FractionBox["1", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}]], RowBox[{"48", " ", RowBox[{"(", RowBox[{"416", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"275", "+", RowBox[{"56", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", RowBox[{"(", RowBox[{ RowBox[{"31", " ", "c", " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{"21", " ", "c", " ", RowBox[{"(", RowBox[{"841", "+", RowBox[{"1640", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{"4", " ", RowBox[{"(", RowBox[{"84", "+", RowBox[{ RowBox[{"(", RowBox[{"5657", "-", RowBox[{"8610", " ", "c"}]}], ")"}], " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "+", RowBox[{"336", " ", RowBox[{"(", RowBox[{"1", "+", RowBox[{"120", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], "+", SuperscriptBox["L2", "4"]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "84"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "5657"}], "+", RowBox[{"8610", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"21", " ", "c", " ", RowBox[{"(", RowBox[{"841", "+", RowBox[{"1640", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "-", RowBox[{"31", " ", "c", " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}]}]}], "+", RowBox[{ FractionBox["1", RowBox[{"29", "+", RowBox[{"70", " ", "c"}]}]], RowBox[{"35", " ", RowBox[{"(", RowBox[{"6", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"2", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"68", "+", RowBox[{"7", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{"3", " ", RowBox[{"(", RowBox[{"638", "-", RowBox[{"215", " ", "c"}]}], ")"}], " ", "c", " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "4"]}], "+", RowBox[{"32", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "363"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "143"}], "+", RowBox[{"20", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q1", "4"]}], "+", RowBox[{"528", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "2"], " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], "+", SuperscriptBox["L2", "4"]}], ")"}], " ", SuperscriptBox["q1", "2"], " ", SuperscriptBox["q2", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"32", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "363"}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "143"}], "+", RowBox[{"20", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{"3", " ", RowBox[{"(", RowBox[{"638", "-", RowBox[{"215", " ", "c"}]}], ")"}], " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["q2", "4"]}]}], ")"}]}]}]}], ")"}], " ", SuperscriptBox["q", "4"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((((( Rational[ 1, 178362777600] $CellContext`c) $CellContext`L1^(-8)) \ ($CellContext`L1 - $CellContext`L2)^2) $CellContext`L2^(-8)) ($CellContext`L1 + \ $CellContext`L2)^2) (( 310032 + $CellContext`c ( 151724 + (35 $CellContext`c) (636 + 35 $CellContext`c))) $CellContext`L1^4 + ((( 2 (18 + 5 $CellContext`c)) ( 11384 + (7 $CellContext`c) (354 + 25 $CellContext`c))) $CellContext`L1^2) $CellContext`L2^2 + \ (310032 + $CellContext`c ( 151724 + (35 $CellContext`c) (636 + 35 $CellContext`c))) $CellContext`L2^4)) Pi^8, 0, (((((Rational[ 1, 185794560] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) ((( 282672 + $CellContext`c ( 263236 + ( 7 (9492 - 235 $CellContext`c)) $CellContext`c)) $CellContext`L2^6) \ $CellContext`q1^2 + ((-282672 + $CellContext`c (-263236 + ( 7 $CellContext`c) (-9492 + 235 $CellContext`c))) $CellContext`L1^6) \ $CellContext`q2^2 + ($CellContext`L1^4 $CellContext`L2^2) (( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) $CellContext`q1^2 + (( 2 (36 + 7 $CellContext`c)) ( 1240 + $CellContext`c (402 + 35 $CellContext`c))) $CellContext`q2^2) + \ ($CellContext`L1^2 $CellContext`L2^4) ((((-2) (36 + 7 $CellContext`c)) ( 1240 + $CellContext`c (402 + 35 $CellContext`c))) $CellContext`q1^2 - ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) $CellContext`q2^2)), ((((( Rational[ 1, 123863040] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) ((( 3046608 + $CellContext`c ( 2235388 + ( 7 (70332 - 685 $CellContext`c)) $CellContext`c)) $CellContext`L2^6) \ $CellContext`q1^3 + ((-3046608 + $CellContext`c (-2235388 + ( 7 $CellContext`c) (-70332 + 685 $CellContext`c))) $CellContext`L1^6) \ $CellContext`q2^3 + ($CellContext`L1^2 $CellContext`L2^4) (((-4) ( 72216 + $CellContext`c ( 37238 + (7 $CellContext`c) (921 + 55 $CellContext`c)))) $CellContext`q1^3 - ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) $CellContext`q2^3) + \ ($CellContext`L1^4 $CellContext`L2^2) (( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) $CellContext`q1^3 + ( 4 (72216 + $CellContext`c ( 37238 + (7 $CellContext`c) (921 + 55 $CellContext`c)))) $CellContext`q2^3)), (((( Rational[ 1, 61931520]/$CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) Pi^8) ((21 ( 216 + $CellContext`c (62 + 5 $CellContext`c))) (($CellContext`L2^4 ((((-21) \ $CellContext`c) (6 + $CellContext`c)) $CellContext`L1^4 + ( 1760 + $CellContext`c (526 + 21 $CellContext`c)) $CellContext`L2^4)) $CellContext`q1^4 - \ ((((160 (22 + 5 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^4) \ $CellContext`q1^2) $CellContext`q2^2 + ($CellContext`L1^4 (( 1760 + $CellContext`c (526 + 21 $CellContext`c)) $CellContext`L1^4 - (( 21 $CellContext`c) ( 6 + $CellContext`c)) $CellContext`L2^4)) \ $CellContext`q2^4) - ((48/(29 + 70 $CellContext`c)) ( 416 + $CellContext`c (275 + 56 $CellContext`c))) (((-$CellContext`L2^2) (( 31 $CellContext`c) $CellContext`L1^6 + ((( 21 $CellContext`c) (841 + 1640 $CellContext`c)) $CellContext`L1^2) \ $CellContext`L2^4 + ( 4 (84 + (5657 - 8610 $CellContext`c) $CellContext`c)) $CellContext`L2^6)) \ $CellContext`q1^4 + ((((( 336 (1 + 120 $CellContext`c)) $CellContext`L1^2) \ $CellContext`L2^2) ($CellContext`L1^4 + $CellContext`L2^4)) \ $CellContext`q1^2) $CellContext`q2^2 + ($CellContext`L1^2 (( 4 (-84 + $CellContext`c (-5657 + 8610 $CellContext`c))) $CellContext`L1^6 - ((( 21 $CellContext`c) (841 + 1640 $CellContext`c)) $CellContext`L1^4) \ $CellContext`L2^2 - ( 31 $CellContext`c) $CellContext`L2^6)) $CellContext`q2^4) + \ ((((35 (6 + $CellContext`c)) (-1 + 2 $CellContext`c)) (68 + 7 $CellContext`c))/(29 + 70 $CellContext`c)) (($CellContext`L2^2 (($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L1^6 + ((( 3 (638 - 215 $CellContext`c)) $CellContext`c) $CellContext`L1^2) \ $CellContext`L2^4 + ( 32 (-363 + $CellContext`c (-143 + 20 $CellContext`c))) $CellContext`L2^6)) \ $CellContext`q1^4 + ((((( 528 (22 + 5 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2) \ ($CellContext`L1^4 + $CellContext`L2^4)) $CellContext`q1^2) $CellContext`q2^2 + \ ($CellContext`L1^2 (( 32 (-363 + $CellContext`c (-143 + 20 $CellContext`c))) $CellContext`L1^6 + ((( 3 (638 - 215 $CellContext`c)) $CellContext`c) $CellContext`L1^4) \ $CellContext`L2^2 + ($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L2^6)) \ $CellContext`q2^4))}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, {(((((Rational[1, 9216] $CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) ($CellContext`L1^2 - $CellContext`L2^2)^2) Pi^4, 0, (((((( Rational[-1, 96] ( 2 + $CellContext`c)) $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^2 + $CellContext`L1^2 \ $CellContext`q2^2), (((((( Rational[-1, 64] ( 2 + $CellContext`c)) $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-4)) ($CellContext`L1 + $CellContext`L2)) Pi^4) ((-$CellContext`L2^2) $CellContext`q1^3 + $CellContext`L1^2 \ $CellContext`q2^3), (((((Rational[-1, 32]/$CellContext`c) ( 2 + $CellContext`c)) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) Pi^4) ((-8) ($CellContext`L2^2 $CellContext`q1^2 - \ $CellContext`L1^2 $CellContext`q2^2)^2 + (($CellContext`c ($CellContext`L1 - \ $CellContext`L2)) ($CellContext`L1 + $CellContext`L2)) ((-$CellContext`L2^2) \ $CellContext`q1^4 + $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {(((((((Rational[1, 4423680] $CellContext`c) ( 4 + $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ($CellContext`L1^2 - $CellContext`L2^2)^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) Pi^6, 0, (((((((Rational[1, 92160] (4 + $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-9) $CellContext`L2^4) $CellContext`q1^2 + ( 9 $CellContext`L1^4) $CellContext`q2^2 + (($CellContext`L1^2 \ $CellContext`L2^2) ($CellContext`q1 - $CellContext`q2)) ($CellContext`q1 + \ $CellContext`q2)), (((((((Rational[1, 61440] (4 + $CellContext`c)) (22 + 5 $CellContext`c)) $CellContext`L1^(-6)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-6)) ($CellContext`L1 + $CellContext`L2)) Pi^6) (((-29) $CellContext`L2^4) $CellContext`q1^3 + ( 29 $CellContext`L1^4) $CellContext`q2^3 + ($CellContext`L1^2 \ $CellContext`L2^2) ($CellContext`q1^3 - $CellContext`q2^3)), ((((( Rational[1, 30720]/$CellContext`c) ( 4 + $CellContext`c)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) Pi^6) (($CellContext`L2^2 (($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L1^4 - ((( 210 $CellContext`c) ( 6 + $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + \ (-3520 + $CellContext`c (438 + 205 $CellContext`c)) $CellContext`L2^4)) $CellContext`q1^4 + \ (((((160 (22 + 5 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2) \ ($CellContext`L1^2 + $CellContext`L2^2)) $CellContext`q1^2) $CellContext`q2^2 + \ ($CellContext`L1^2 ((-3520 + $CellContext`c (438 + 205 $CellContext`c)) $CellContext`L1^4 - ((( 210 $CellContext`c) ( 6 + $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2 + \ ($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L2^4)) $CellContext`q2^4)}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {(((((( Rational[ 1, 178362777600] $CellContext`c) $CellContext`L1^(-8)) \ ($CellContext`L1 - $CellContext`L2)^2) $CellContext`L2^(-8)) ($CellContext`L1 + \ $CellContext`L2)^2) (( 310032 + $CellContext`c ( 151724 + (35 $CellContext`c) (636 + 35 $CellContext`c))) $CellContext`L1^4 + ((( 2 (18 + 5 $CellContext`c)) ( 11384 + (7 $CellContext`c) (354 + 25 $CellContext`c))) $CellContext`L1^2) $CellContext`L2^2 + \ (310032 + $CellContext`c ( 151724 + (35 $CellContext`c) (636 + 35 $CellContext`c))) $CellContext`L2^4)) Pi^8, 0, (((((Rational[ 1, 185794560] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) ((( 282672 + $CellContext`c ( 263236 + ( 7 (9492 - 235 $CellContext`c)) $CellContext`c)) $CellContext`L2^6) \ $CellContext`q1^2 + ((-282672 + $CellContext`c (-263236 + ( 7 $CellContext`c) (-9492 + 235 $CellContext`c))) $CellContext`L1^6) $CellContext`q2^2 + \ ($CellContext`L1^4 $CellContext`L2^2) (( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) $CellContext`q1^2 + (( 2 (36 + 7 $CellContext`c)) ( 1240 + $CellContext`c (402 + 35 $CellContext`c))) $CellContext`q2^2) + \ ($CellContext`L1^2 $CellContext`L2^4) ((((-2) (36 + 7 $CellContext`c)) ( 1240 + $CellContext`c (402 + 35 $CellContext`c))) $CellContext`q1^2 - ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) $CellContext`q2^2)), ((((( Rational[ 1, 123863040] $CellContext`L1^(-8)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-8)) ($CellContext`L1 + $CellContext`L2)) Pi^8) ((( 3046608 + $CellContext`c ( 2235388 + ( 7 (70332 - 685 $CellContext`c)) $CellContext`c)) $CellContext`L2^6) \ $CellContext`q1^3 + ((-3046608 + $CellContext`c (-2235388 + ( 7 $CellContext`c) (-70332 + 685 $CellContext`c))) $CellContext`L1^6) $CellContext`q2^3 + \ ($CellContext`L1^2 $CellContext`L2^4) (((-4) ( 72216 + $CellContext`c ( 37238 + (7 $CellContext`c) (921 + 55 $CellContext`c)))) $CellContext`q1^3 - ( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) $CellContext`q2^3) + ($CellContext`L1^4 \ $CellContext`L2^2) (( 10512 + $CellContext`c ( 5020 + (7 $CellContext`c) (96 + 5 $CellContext`c))) $CellContext`q1^3 + ( 4 (72216 + $CellContext`c ( 37238 + (7 $CellContext`c) (921 + 55 $CellContext`c)))) $CellContext`q2^3)), (((( Rational[ 1, 61931520]/$CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) Pi^8) ((21 ( 216 + $CellContext`c (62 + 5 $CellContext`c))) (($CellContext`L2^4 ((((-21) \ $CellContext`c) (6 + $CellContext`c)) $CellContext`L1^4 + ( 1760 + $CellContext`c (526 + 21 $CellContext`c)) $CellContext`L2^4)) $CellContext`q1^4 - \ ((((160 (22 + 5 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^4) \ $CellContext`q1^2) $CellContext`q2^2 + ($CellContext`L1^4 (( 1760 + $CellContext`c (526 + 21 $CellContext`c)) $CellContext`L1^4 - (( 21 $CellContext`c) ( 6 + $CellContext`c)) $CellContext`L2^4)) $CellContext`q2^4) - \ ((48/(29 + 70 $CellContext`c)) ( 416 + $CellContext`c (275 + 56 $CellContext`c))) (((-$CellContext`L2^2) (( 31 $CellContext`c) $CellContext`L1^6 + ((( 21 $CellContext`c) (841 + 1640 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^4 + \ (4 (84 + (5657 - 8610 $CellContext`c) $CellContext`c)) $CellContext`L2^6)) \ $CellContext`q1^4 + ((((( 336 (1 + 120 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2) \ ($CellContext`L1^4 + $CellContext`L2^4)) $CellContext`q1^2) $CellContext`q2^2 + \ ($CellContext`L1^2 (( 4 (-84 + $CellContext`c (-5657 + 8610 $CellContext`c))) $CellContext`L1^6 - ((( 21 $CellContext`c) (841 + 1640 $CellContext`c)) $CellContext`L1^4) $CellContext`L2^2 - \ (31 $CellContext`c) $CellContext`L2^6)) $CellContext`q2^4) + (((( 35 (6 + $CellContext`c)) (-1 + 2 $CellContext`c)) (68 + 7 $CellContext`c))/(29 + 70 $CellContext`c)) (($CellContext`L2^2 (($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L1^6 + ((( 3 (638 - 215 $CellContext`c)) $CellContext`c) $CellContext`L1^2) \ $CellContext`L2^4 + ( 32 (-363 + $CellContext`c (-143 + 20 $CellContext`c))) $CellContext`L2^6)) \ $CellContext`q1^4 + ((((( 528 (22 + 5 $CellContext`c)) $CellContext`L1^2) $CellContext`L2^2) \ ($CellContext`L1^4 + $CellContext`L2^4)) $CellContext`q1^2) $CellContext`q2^2 + \ ($CellContext`L1^2 (( 32 (-363 + $CellContext`c (-143 + 20 $CellContext`c))) $CellContext`L1^6 + ((( 3 (638 - 215 $CellContext`c)) $CellContext`c) $CellContext`L1^4) \ $CellContext`L2^2 + ($CellContext`c (22 + 5 $CellContext`c)) $CellContext`L2^6)) \ $CellContext`q2^4))}, 0, 5, 1]}, 4, 10, 1], Editable->False], ")"}]}]}], ";"}]], "Input", CellChangeTimes->{{3.7041177096676693`*^9, 3.704117722947776*^9}, 3.7041200520732484`*^9, 3.7041200892496595`*^9, {3.7041256489764595`*^9, 3.7041256504155164`*^9}, {3.7041268672817106`*^9, 3.704126883505083*^9}, { 3.7041279326025686`*^9, 3.7041279339044714`*^9}, 3.704129365872342*^9, { 3.7041294373000555`*^9, 3.704129471598628*^9}, 3.7041296599213877`*^9, 3.7041304063254724`*^9, 3.704132036287876*^9}] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Section 3.3 Schatten 4-norm", "Section", CellChangeTimes->{{3.7039542022131257`*^9, 3.703954219345484*^9}, { 3.7039553305656457`*^9, 3.703955332918915*^9}, {3.704042560801203*^9, 3.704042566640339*^9}, {3.704120014430778*^9, 3.704120020367242*^9}, { 3.704120063669981*^9, 3.7041200710617695`*^9}, 3.7041202585198755`*^9, { 3.704126824559267*^9, 3.704126842406231*^9}, 3.7041293515724216`*^9, { 3.704129387492532*^9, 3.7041293906268845`*^9}, 3.7041294512958555`*^9, 3.704172903935352*^9, {3.7118131062336793`*^9, 3.7118131082978272`*^9}, { 3.711906516656229*^9, 3.7119065177437487`*^9}}], Cell[CellGroupData[{ Cell["||\[Rho]_A(L1,\[Phi]1)-\[Rho]_A(L2,\[Phi]2)||_4^4", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, 3.704120023776886*^9, {3.704120076714172*^9, 3.704120078900853*^9}, { 3.704126845060828*^9, 3.7041268452944665`*^9}, {3.704129395817523*^9, 3.7041294538824053`*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"L1\[Phi]1L2\[Phi]244", "=", RowBox[{ SuperscriptBox["\[ScriptL]", RowBox[{ RowBox[{"-", "5"}], RowBox[{"c", "/", "16"}]}]], RowBox[{"(", RowBox[{ RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"192", "+", RowBox[{"25", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14"}], "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]2"}]}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]1"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], "4"], " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"21743271936", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], SuperscriptBox["\[ScriptL]", "8"]}], "+", SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"]}], ")"}]}]}], ";"}]], "Input", CellChangeTimes->{{3.704042631409958*^9, 3.704042659643123*^9}, 3.7041200337358904`*^9, 3.7041200746500072`*^9, {3.704124558584817*^9, 3.7041245601233606`*^9}, {3.704126857355027*^9, 3.7041269027230988`*^9}, 3.7041293580461025`*^9, {3.7041294329946194`*^9, 3.7041294598182554`*^9}, { 3.7041296619586*^9, 3.704129672185783*^9}, 3.704130408074617*^9, { 3.7041331597001686`*^9, 3.70413318827296*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["||\[Rho]_A(L1,\[Phi]),\[Rho]_A(L2,q)||_4^4", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, 3.7041200258581767`*^9, { 3.7041200815416093`*^9, 3.7041200819048214`*^9}, 3.704126849767155*^9, { 3.7041294033741727`*^9, 3.7041294213640456`*^9}, {3.7041294546670923`*^9, 3.704129455599429*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"L1\[Phi]L2q44", "=", RowBox[{ SuperscriptBox["\[ScriptL]", RowBox[{ RowBox[{"-", "5"}], RowBox[{"c", "/", "16"}]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"192", "+", RowBox[{"25", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14"}], "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "4"], " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"21743271936", " ", SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"192", "+", RowBox[{"25", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14"}], "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "3"], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"113246208", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"192", "+", RowBox[{"25", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14"}], "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "3"], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"75497472", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"192", "+", RowBox[{"25", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14"}], "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "24"}], "+", "c"}], ")"}], " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "8"]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"37748736", " ", RowBox[{"(", RowBox[{ SuperscriptBox["c", "3"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((((Rational[1, 21743271936] $CellContext`c^(-3)) ( 2 + $CellContext`c)) ( 192 + (25 $CellContext`c) (-14 + 25 $CellContext`c))) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^4) Pi^8, 0, ((((((Rational[-1, 113246208] $CellContext`c^(-3)) ( 2 + $CellContext`c)) ( 192 + (25 $CellContext`c) (-14 + 25 $CellContext`c))) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^3) Pi^8, ((((((Rational[-1, 75497472] $CellContext`c^(-3)) ( 2 + $CellContext`c)) ( 192 + (25 $CellContext`c) (-14 + 25 $CellContext`c))) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^3) Pi^8, (((((((Rational[-1, 37748736] $CellContext`c^(-3)) ( 2 + $CellContext`c)) ( 192 + (25 $CellContext`c) (-14 + 25 $CellContext`c))) $CellContext`L1^(-6)) \ $CellContext`L2^(-8)) ((-24 + $CellContext`c) $CellContext`L1^2 - \ ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^8}, 0, 5, 1], Editable->False], ")"}], SuperscriptBox["\[ScriptL]", "8"]}], "+", SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"]}], ")"}]}]}], ";"}]], "Input", CellChangeTimes->{{3.7041154839401503`*^9, 3.7041155058482423`*^9}, 3.7041200391757126`*^9, 3.70412009230025*^9, {3.7041249457334986`*^9, 3.704124946982025*^9}, {3.704126863198118*^9, 3.7041268827047496`*^9}, { 3.7041272877963457`*^9, 3.704127288633995*^9}, 3.7041293622530575`*^9, { 3.704129434731191*^9, 3.704129469564992*^9}, 3.7041296893338137`*^9, 3.7041304087075167`*^9, 3.704133177016971*^9, {3.704133501147785*^9, 3.704133503066388*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["||\[Rho]_A(L1,q1)-\[Rho]_A(L2,q2)||_4^4", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, {3.704116595159308*^9, 3.704116597929334*^9}, {3.7041177049986935`*^9, 3.704117707948104*^9}, 3.704120028560308*^9, {3.704120086479438*^9, 3.7041200867951765`*^9}, 3.7041268511846633`*^9, {3.704129409635429*^9, 3.70412945763129*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"L1q1L2q244", "=", RowBox[{ SuperscriptBox["\[ScriptL]", RowBox[{ RowBox[{"-", "5"}], RowBox[{"c", "/", "16"}]}]], RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"192", "+", RowBox[{"25", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14"}], "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], "4"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], "4"], " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"21743271936", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"192", "+", RowBox[{"25", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14"}], "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], "3"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], "3"], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "2"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "2"]}], RowBox[{"113246208", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"192", "+", RowBox[{"25", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14"}], "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], "3"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], "3"], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "3"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "3"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "3"]}], RowBox[{"75497472", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"2", "+", "c"}], ")"}], " ", RowBox[{"(", RowBox[{"192", "+", RowBox[{"25", " ", "c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "14"}], "+", RowBox[{"25", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "8"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "24"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{ SuperscriptBox["L2", "2"], " ", SuperscriptBox["q1", "2"]}], "-", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "2"]}]}], ")"}], "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", SuperscriptBox["L2", "2"]}], " ", SuperscriptBox["q1", "4"]}], "+", RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["q2", "4"]}]}], ")"}]}]}], ")"}]}], ")"}], " ", SuperscriptBox["q", "4"]}], RowBox[{"37748736", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}], ")"}]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {(((((((Rational[1, 21743271936] $CellContext`c) ( 2 + $CellContext`c)) ( 192 + (25 $CellContext`c) (-14 + 25 $CellContext`c))) $CellContext`L1^(-8)) \ ($CellContext`L1 - $CellContext`L2)^4) $CellContext`L2^(-8)) ($CellContext`L1 + \ $CellContext`L2)^4) Pi^8, 0, (((((((Rational[-1, 113246208] (2 + $CellContext`c)) ( 192 + (25 $CellContext`c) (-14 + 25 $CellContext`c))) $CellContext`L1^(-8)) \ ($CellContext`L1 - $CellContext`L2)^3) $CellContext`L2^(-8)) ($CellContext`L1 + \ $CellContext`L2)^3) Pi^8) ((-$CellContext`L2^2) $CellContext`q1^2 + $CellContext`L1^2 \ $CellContext`q2^2), (((((((Rational[-1, 75497472] (2 + $CellContext`c)) ( 192 + (25 $CellContext`c) (-14 + 25 $CellContext`c))) $CellContext`L1^(-8)) \ ($CellContext`L1 - $CellContext`L2)^3) $CellContext`L2^(-8)) ($CellContext`L1 + \ $CellContext`L2)^3) Pi^8) ((-$CellContext`L2^2) $CellContext`q1^3 + $CellContext`L1^2 \ $CellContext`q2^3), ((((((((Rational[-1, 37748736]/$CellContext`c) ( 2 + $CellContext`c)) ( 192 + (25 $CellContext`c) (-14 + 25 $CellContext`c))) $CellContext`L1^(-8)) \ ($CellContext`L1 - $CellContext`L2)^2) $CellContext`L2^(-8)) ($CellContext`L1 + \ $CellContext`L2)^2) Pi^8) ((-24) ($CellContext`L2^2 $CellContext`q1^2 - \ $CellContext`L1^2 $CellContext`q2^2)^2 + (($CellContext`c ($CellContext`L1 - \ $CellContext`L2)) ($CellContext`L1 + $CellContext`L2)) ((-$CellContext`L2^2) \ $CellContext`q1^4 + $CellContext`L1^2 $CellContext`q2^4))}, 0, 5, 1], Editable->False], ")"}], SuperscriptBox["\[ScriptL]", "8"]}], "+", SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"]}], ")"}]}]}], ";"}]], "Input", CellChangeTimes->{{3.7041177096676693`*^9, 3.704117722947776*^9}, 3.7041200520732484`*^9, 3.7041200892496595`*^9, {3.7041256489764595`*^9, 3.7041256504155164`*^9}, {3.7041268672817106`*^9, 3.704126883505083*^9}, { 3.7041279326025686`*^9, 3.7041279339044714`*^9}, 3.704129365872342*^9, { 3.7041294373000555`*^9, 3.704129468843072*^9}, 3.7041296908358326`*^9, 3.704130409975577*^9, 3.7041331784342794`*^9, {3.7041340719018087`*^9, 3.7041340828135223`*^9}}] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Section 4 Check of ETH", "Section", CellChangeTimes->{{3.7039542022131257`*^9, 3.703954219345484*^9}, { 3.7039553305656457`*^9, 3.703955332918915*^9}, {3.704042560801203*^9, 3.704042566640339*^9}, {3.704120014430778*^9, 3.704120020367242*^9}, { 3.704120063669981*^9, 3.7041200710617695`*^9}, 3.7041202585198755`*^9, { 3.704126824559267*^9, 3.704126842406231*^9}, 3.7041293515724216`*^9, { 3.704129387492532*^9, 3.7041293906268845`*^9}, 3.7041294512958555`*^9, { 3.704168991384746*^9, 3.704168999763732*^9}, 3.7041729052509613`*^9, { 3.711813111397418*^9, 3.7118131382619553`*^9}}], Cell[CellGroupData[{ Cell["difference of Renyi entropy", "Subsection", CellChangeTimes->{{3.7037783236359653`*^9, 3.703778329224622*^9}, { 3.704168737387566*^9, 3.704168741823089*^9}}], Cell[BoxData[ RowBox[{ InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"], " ", SubscriptBox["\[Epsilon]", "\[Phi]"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", RowBox[{"22", " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], RowBox[{"90", " ", SuperscriptBox["L", "4"], " ", SuperscriptBox["n", "3"]}]], "-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "6"], " ", SubscriptBox["\[Epsilon]", "\[Phi]"], " ", RowBox[{"(", RowBox[{"2", "+", RowBox[{"4", " ", SuperscriptBox["n", "2"]}], "-", RowBox[{"3", " ", RowBox[{"(", RowBox[{"37", "+", RowBox[{"46", " ", SuperscriptBox["n", "2"]}]}], ")"}], " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}], "+", RowBox[{"8", " ", RowBox[{"(", RowBox[{"188", "+", RowBox[{"145", " ", SuperscriptBox["n", "2"]}]}], ")"}], " ", SubsuperscriptBox["\[Epsilon]", "\[Phi]", "2"]}]}], ")"}]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], RowBox[{"2835", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L", "6"], " ", SuperscriptBox["n", "5"]}], ")"}]}]], "+", RowBox[{ FractionBox["1", RowBox[{"56700", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "7"]}]], RowBox[{"c", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SubscriptBox["\[Epsilon]", "\[Phi]"], " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", SuperscriptBox["n", "2"], "+", SuperscriptBox["n", "4"], "-", RowBox[{"3", " ", SuperscriptBox["n", "6"]}]}], ")"}]}], "+", RowBox[{"2", " ", SubscriptBox["\[Epsilon]", "\[Phi]"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "4312"}], "-", RowBox[{"753", " ", "c"}], "-", RowBox[{ RowBox[{"(", RowBox[{"1072", "+", RowBox[{"213", " ", "c"}]}], ")"}], " ", SuperscriptBox["n", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{"400", "+", RowBox[{"87", " ", "c"}]}], ")"}], " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"3", " ", RowBox[{"(", RowBox[{"1544", "+", RowBox[{"351", " ", "c"}]}], ")"}], " ", SuperscriptBox["n", "6"]}], "+", RowBox[{"4", " ", SubscriptBox["\[Epsilon]", "\[Phi]"], " ", RowBox[{"(", RowBox[{ RowBox[{ RowBox[{"-", "c"}], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"5863", "+", RowBox[{"4636", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"4333", " ", SuperscriptBox["n", "4"]}]}], ")"}]}], "-", RowBox[{"44", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "836"}], "+", RowBox[{"89", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"26", " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"433", " ", SuperscriptBox["n", "6"]}]}], ")"}]}], "+", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{"58213", "+", RowBox[{"24286", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"25933", " ", SuperscriptBox["n", "4"]}]}], ")"}]}], "+", RowBox[{"88", " ", RowBox[{"(", RowBox[{ RowBox[{"-", "4284"}], "+", RowBox[{"1511", " ", SuperscriptBox["n", "2"]}], "-", RowBox[{"106", " ", SuperscriptBox["n", "4"]}], "+", RowBox[{"1295", " ", SuperscriptBox["n", "6"]}]}], ")"}]}]}], ")"}], " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[1, 90] $CellContext`c $CellContext`L^(-4) (-1 + $CellContext`n) \ $CellContext`n^(-3) (1 + $CellContext`n)^2 Pi^4 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]] (-1 + 22 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]), 0, Rational[-1, 2835] $CellContext`c $CellContext`L^(-6) (-1 + $CellContext`n) \ $CellContext`n^(-5) (1 + $CellContext`n)^2 Pi^6 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]] (2 + 4 $CellContext`n^2 - 3 (37 + 46 $CellContext`n^2) Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]] + 8 (188 + 145 $CellContext`n^2) Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]^2), 0, Rational[1, 56700] $CellContext`c (22 + 5 $CellContext`c)^(-1) $CellContext`L^(-8) $CellContext`n^(-7) ( 1 + $CellContext`n) Pi^8 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]] ( 3 (22 + 5 $CellContext`c) (1 + $CellContext`n^2 + $CellContext`n^4 - 3 $CellContext`n^6) + 2 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]] (-4312 - 753 $CellContext`c - (1072 + 213 $CellContext`c) $CellContext`n^2 - ( 400 + 87 $CellContext`c) $CellContext`n^4 + 3 (1544 + 351 $CellContext`c) $CellContext`n^6 + 4 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]] \ (-$CellContext`c (-1 + $CellContext`n) (1 + $CellContext`n) (5863 + 4636 $CellContext`n^2 + 4333 $CellContext`n^4) - 44 (-836 + 89 $CellContext`n^2 + 26 $CellContext`n^4 + 433 $CellContext`n^6) + ($CellContext`c (-1 + $CellContext`n) ( 1 + $CellContext`n) (58213 + 24286 $CellContext`n^2 + 25933 $CellContext`n^4) + 88 (-4284 + 1511 $CellContext`n^2 - 106 $CellContext`n^4 + 1295 $CellContext`n^6)) Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]])))}, 4, 10, 1], Editable->False], ";"}]], "Input", CellChangeTimes->{{3.7041687317983127`*^9, 3.7041687318611035`*^9}, { 3.7041711746570997`*^9, 3.7041711810623875`*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["difference of entanglement entropy", "Subsection", CellChangeTimes->{{3.7037783236359653`*^9, 3.703778329224622*^9}, { 3.7037788262162514`*^9, 3.7037788361382904`*^9}, {3.704168745744298*^9, 3.7041687504839993`*^9}}], Cell[BoxData[ RowBox[{ InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{"128", " ", RowBox[{"(", RowBox[{"c", " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"22", " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}], "2"], " ", SubsuperscriptBox["\[Epsilon]", "\[Phi]", "2"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], RowBox[{"1575", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"]}], ")"}]}]]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 8, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[-128, 1575] $CellContext`c (22 + 5 $CellContext`c)^(-1) $CellContext`L^(-8) Pi^8 (1 - 22 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]])^2 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]^2}, 8, 10, 1], Editable->False], ";"}]], "Input", CellChangeTimes->{{3.704168762143138*^9, 3.704168762158573*^9}, 3.7041711718565116`*^9, 3.7041715262134085`*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Relative entropy S(\[Rho]_A(L,\[Phi])||\[Rho]_A(\[Beta]))", "Subsection", CellChangeTimes->{{3.7037789432503147`*^9, 3.703778971804765*^9}}], Cell[BoxData[ RowBox[{ InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"128", " ", "c", " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"22", " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}], "2"], " ", SubsuperscriptBox["\[Epsilon]", "\[Phi]", "2"], " ", SuperscriptBox["\[ScriptL]", "8"]}], RowBox[{"1575", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 8, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[128, 1575] $CellContext`c (22 + 5 $CellContext`c)^(-1) $CellContext`L^(-8) Pi^8 (1 - 22 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]])^2 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]^2}, 8, 10, 1], Editable->False], ";"}]], "Input", CellChangeTimes->{{3.704168797644693*^9, 3.7041687976601396`*^9}, 3.7041711707403836`*^9, 3.704171662147021*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Relative entropy S(\[Rho]_A(\[Beta])||\[Rho]_A(L,\[Phi]))", "Subsection", CellChangeTimes->{{3.7037789432503147`*^9, 3.703778971804765*^9}, { 3.703779456158281*^9, 3.703779461046525*^9}, 3.7037801168524857`*^9}], Cell[BoxData[ RowBox[{ InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"128", " ", "c", " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"22", " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}], "2"], " ", SubsuperscriptBox["\[Epsilon]", "\[Phi]", "2"], " ", SuperscriptBox["\[ScriptL]", "8"]}], RowBox[{"1575", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 8, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[128, 1575] $CellContext`c (22 + 5 $CellContext`c)^(-1) $CellContext`L^(-8) Pi^8 (1 - 22 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]])^2 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]^2}, 8, 10, 1], Editable->False], ";"}]], "Input", CellChangeTimes->{{3.704168825761334*^9, 3.7041688257771215`*^9}, 3.704171169007971*^9, 3.704171664317585*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Symmetrized relative entropy S(\[Rho]_A(L,\[Phi]),\[Rho]_A(\[Beta]))", \ "Subsection", CellChangeTimes->{{3.7037789432503147`*^9, 3.703778971804765*^9}, { 3.7037801692520647`*^9, 3.7037801726307435`*^9}, 3.7037802145104*^9, { 3.704168839539097*^9, 3.704168848762682*^9}}], Cell[BoxData[ RowBox[{ InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"256", " ", "c", " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"22", " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}], "2"], " ", SubsuperscriptBox["\[Epsilon]", "\[Phi]", "2"], " ", SuperscriptBox["\[ScriptL]", "8"]}], RowBox[{"1575", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 8, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[256, 1575] $CellContext`c (22 + 5 $CellContext`c)^(-1) $CellContext`L^(-8) Pi^8 (1 - 22 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]])^2 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]^2}, 8, 10, 1], Editable->False], ";"}]], "Input", CellChangeTimes->{{3.704168875126713*^9, 3.70416887514236*^9}, 3.704171167706422*^9, 3.704171748878195*^9}] }, Closed]], Cell[CellGroupData[{ Cell["2nd symmetrized relative entropy \ S_2(\[Rho]_A(L,\[Phi]),\[Rho]_A(\[Beta]))", "Subsection", CellChangeTimes->{{3.7037789432503147`*^9, 3.703778971804765*^9}, { 3.7037801692520647`*^9, 3.7037801726307435`*^9}, 3.7037802145104*^9, { 3.703780380713605*^9, 3.703780386265332*^9}, 3.7037804674765506`*^9, { 3.7041688826660337`*^9, 3.704168883698132*^9}}], Cell[BoxData[ RowBox[{ InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"27", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"22", " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}], "2"], " ", SubsuperscriptBox["\[Epsilon]", "\[Phi]", "2"], " ", SuperscriptBox["\[ScriptL]", "8"]}], RowBox[{"3200", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 8, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[1, 3200] $CellContext`c (22 + 5 $CellContext`c)^(-1) (27 + 5 $CellContext`c) $CellContext`L^(-8) Pi^8 (1 - 22 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]])^2 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]^2}, 8, 10, 1], Editable->False], ";"}]], "Input", CellChangeTimes->{{3.7041688947768245`*^9, 3.704168894792238*^9}, 3.7041711660898094`*^9, 3.704172218227645*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Jensen-Renyi divergence JR_n(\[Rho]_A(L,\[Phi]),\[Rho]_A(\[Beta]))", \ "Subsection", CellChangeTimes->{{3.7037789432503147`*^9, 3.703778971804765*^9}, { 3.7037801692520647`*^9, 3.7037801726307435`*^9}, 3.7037802145104*^9, { 3.703780380713605*^9, 3.703780386265332*^9}, 3.7037804674765506`*^9, { 3.7037804981620235`*^9, 3.7037805119198985`*^9}, 3.703780579628423*^9, { 3.7037811180279474`*^9, 3.703781123826932*^9}}], Cell[BoxData[ RowBox[{ InterpretationBox[ RowBox[{ RowBox[{"-", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{"c", " ", RowBox[{"(", RowBox[{"1", "+", "n"}], ")"}], " ", RowBox[{"(", RowBox[{ RowBox[{"175", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["n", "2"]}], ")"}], "3"]}], "+", RowBox[{"70", " ", "c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"-", "1"}], "+", SuperscriptBox["n", "2"]}], ")"}], "2"], " ", RowBox[{"(", RowBox[{ RowBox[{"-", "55"}], "+", RowBox[{"7", " ", SuperscriptBox["n", "2"]}]}], ")"}]}], "-", RowBox[{"8", " ", RowBox[{"(", RowBox[{"11", "+", SuperscriptBox["n", "2"]}], ")"}], " ", RowBox[{"(", RowBox[{"381", "-", RowBox[{"298", " ", SuperscriptBox["n", "2"]}], "+", RowBox[{"157", " ", SuperscriptBox["n", "4"]}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"22", " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}], "2"], " ", SubsuperscriptBox["\[Epsilon]", "\[Phi]", "2"]}], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], RowBox[{"2268000", " ", RowBox[{"(", RowBox[{ RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"], " ", SuperscriptBox["n", "7"]}], ")"}]}]]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 8, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[-1, 2268000] $CellContext`c (22 + 5 $CellContext`c)^(-1) $CellContext`L^(-8) $CellContext`n^(-7) ( 1 + $CellContext`n) (175 $CellContext`c^2 (-1 + $CellContext`n^2)^3 + 70 $CellContext`c (-1 + $CellContext`n^2)^2 (-55 + 7 $CellContext`n^2) - 8 (11 + $CellContext`n^2) (381 - 298 $CellContext`n^2 + 157 $CellContext`n^4)) Pi^8 (1 - 22 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]])^2 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]^2}, 8, 10, 1], Editable->False], ";"}]], "Input", CellChangeTimes->{{3.7041689025685196`*^9, 3.704168902615186*^9}, 3.704171164219508*^9, 3.704172377123266*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Jensen-Shannon divergence JS(\[Rho]_A(L,\[Phi]),\[Rho]_A(\[Beta]))", \ "Subsection", CellChangeTimes->{{3.7037789432503147`*^9, 3.703778971804765*^9}, { 3.7037801692520647`*^9, 3.7037801726307435`*^9}, 3.7037802145104*^9, { 3.703780380713605*^9, 3.703780386265332*^9}, 3.7037804674765506`*^9, { 3.7037804981620235`*^9, 3.7037805119198985`*^9}, 3.703780579628423*^9}], Cell[BoxData[ RowBox[{ InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"32", " ", "c", " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"22", " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}], "2"], " ", SubsuperscriptBox["\[Epsilon]", "\[Phi]", "2"], " ", SuperscriptBox["\[ScriptL]", "8"]}], RowBox[{"1575", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 8, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[32, 1575] $CellContext`c (22 + 5 $CellContext`c)^(-1) $CellContext`L^(-8) Pi^8 (1 - 22 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]])^2 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]^2}, 8, 10, 1], Editable->False], ";"}]], "Input", CellChangeTimes->{{3.7041689152298107`*^9, 3.704168915251771*^9}, 3.7041711628490353`*^9, 3.704172722126026*^9}] }, Closed]], Cell[CellGroupData[{ Cell["Schatten 2-norm ||\[Rho]_A(L,\[Phi])-\[Rho]_A(\[Beta])||_2^2", \ "Subsection", CellChangeTimes->{{3.7037789432503147`*^9, 3.703778971804765*^9}, { 3.7037801692520647`*^9, 3.7037801726307435`*^9}, 3.7037802145104*^9, { 3.703780380713605*^9, 3.703780386265332*^9}, 3.7037804674765506`*^9, { 3.7037804981620235`*^9, 3.7037805119198985`*^9}, 3.703780579628423*^9, { 3.7037813542842693`*^9, 3.703781370179696*^9}, {3.703781561675321*^9, 3.7037815719153194`*^9}, {3.704170932943373*^9, 3.704170952266959*^9}, { 3.711906536506302*^9, 3.71190653736814*^9}}], Cell[BoxData[ RowBox[{ RowBox[{ SuperscriptBox["\[ScriptL]", RowBox[{ RowBox[{"-", "c"}], "/", "8"}]], RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{"216", "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"62", "+", RowBox[{"5", " ", "c"}]}], ")"}]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox[ RowBox[{"(", RowBox[{"1", "-", RowBox[{"22", " ", SubscriptBox["\[Epsilon]", "\[Phi]"]}]}], ")"}], "2"], " ", SubsuperscriptBox["\[Epsilon]", "\[Phi]", "2"], " ", SuperscriptBox["\[ScriptL]", "8"]}], RowBox[{"25600", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L", "8"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 8, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { Rational[1, 25600] $CellContext`c (22 + 5 $CellContext`c)^(-1) ( 216 + $CellContext`c (62 + 5 $CellContext`c)) $CellContext`L^(-8) Pi^8 (1 - 22 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]])^2 Subscript[$CellContext`\[Epsilon], $CellContext`\[Phi]]^2}, 8, 10, 1], Editable->False], ")"}]}], ";"}]], "Input", CellChangeTimes->{{3.7041689435967026`*^9, 3.7041689436122336`*^9}, 3.7041711614326267`*^9, {3.7041728419211044`*^9, 3.704172866641865*^9}}] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell["Appendix A Relative entropy from modular Hamiltonian", "Section", CellChangeTimes->{{3.7039542022131257`*^9, 3.703954219345484*^9}, { 3.7039553305656457`*^9, 3.703955332918915*^9}, {3.704042560801203*^9, 3.704042566640339*^9}, {3.7041682598710337`*^9, 3.7041682722348256`*^9}, 3.7041729067038827`*^9, {3.7118131440411043`*^9, 3.7118131481239586`*^9}}], Cell[CellGroupData[{ Cell["S(\[Rho]_A(L1,\[Phi])||\[Rho]_A(L2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.7041682929223022`*^9, 3.704168295722787*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SL1\[Phi]L2\[Phi]", "=", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{ SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["\[ScriptL]", "4"]}], RowBox[{"1080", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"2", " ", "c", " ", SuperscriptBox["L1", "2"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"c", "-", RowBox[{"24", " ", "h\[Phi]"}]}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox[ RowBox[{"(", RowBox[{ RowBox[{"24", " ", "h\[Phi]", " ", SuperscriptBox["L2", "2"]}], "+", RowBox[{"c", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}]}]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["\[ScriptL]", "6"]}], RowBox[{"17010", " ", SuperscriptBox["c", "2"], " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{ RowBox[{"(", RowBox[{ FractionBox[ RowBox[{ RowBox[{ SuperscriptBox["c", "4"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}]}], "-", RowBox[{"96", " ", SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", "h\[Phi]"}], "+", RowBox[{"1152", " ", SuperscriptBox["c", "2"], " ", RowBox[{"(", RowBox[{"82", "+", RowBox[{"15", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "2"]}], "-", RowBox[{"92160", " ", "c", " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"3", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "3"]}], "+", RowBox[{"184320", " ", RowBox[{"(", RowBox[{"88", "+", RowBox[{"9", " ", "c"}]}], ")"}], " ", SuperscriptBox["h\[Phi]", "4"]}]}], RowBox[{ SuperscriptBox["c", "3"], " ", RowBox[{"(", RowBox[{"22", "+", RowBox[{"5", " ", "c"}]}], ")"}], " ", SuperscriptBox["L1", "8"]}]], "+", FractionBox[ RowBox[{"3", " ", "c"}], SuperscriptBox["L2", "8"]], "-", FractionBox[ RowBox[{"4", " ", "c"}], RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{"96", " ", "h\[Phi]"}], RowBox[{ SuperscriptBox["L1", "2"], " ", SuperscriptBox["L2", "6"]}]]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["\[ScriptL]", "8"]}], "226800"], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, {((((Rational[ 1, 1080]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^4, 0, ((((( Rational[ 1, 17010] $CellContext`c^(-2)) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ((2 $CellContext`c) $CellContext`L1^2 + ($CellContext`c - 24 $CellContext`h\[Phi]) $CellContext`L2^2)) (( 24 $CellContext`h\[Phi]) $CellContext`L2^2 + ($CellContext`c \ ($CellContext`L1 - $CellContext`L2)) ($CellContext`L1 + $CellContext`L2))^2) Pi^6, 0, ( Rational[ 1, 226800] ((($CellContext`c^(-3)/(22 + 5 $CellContext`c)) ($CellContext`c^4 (22 + 5 $CellContext`c) - (( 96 $CellContext`c^3) (22 + 5 $CellContext`c)) $CellContext`h\[Phi] + (( 1152 $CellContext`c^2) (82 + 15 $CellContext`c)) $CellContext`h\[Phi]^2 - (( 92160 $CellContext`c) (22 + 3 $CellContext`c)) $CellContext`h\[Phi]^3 + ( 184320 (88 + 9 $CellContext`c)) $CellContext`h\[Phi]^4)) \ $CellContext`L1^(-8) + (3 $CellContext`c) $CellContext`L2^(-8) - (( 4 $CellContext`c) $CellContext`L1^(-2)) $CellContext`L2^(-6) + (( 96 $CellContext`h\[Phi]) $CellContext`L1^(-2)) \ $CellContext`L2^(-6))) Pi^8}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.704042631409958*^9, 3.704042659643123*^9}, { 3.7041683134929705`*^9, 3.7041683187841167`*^9}, {3.704188899216917*^9, 3.70418892013902*^9}}] }, Closed]], Cell[CellGroupData[{ Cell["S(\[Rho]_A(L1,q)||\[Rho]_A(L2))", "Subsection", CellChangeTimes->{{3.7039542261844387`*^9, 3.703954259269836*^9}, { 3.7040425787917786`*^9, 3.7040426121890187`*^9}, 3.704043482955864*^9, { 3.704115479974535*^9, 3.7041154819918647`*^9}, {3.704116595159308*^9, 3.704116597929334*^9}, {3.7041177049986935`*^9, 3.704117707948104*^9}, { 3.704168303412092*^9, 3.70416830548335*^9}}], Cell[BoxData[ RowBox[{ RowBox[{"SL1qL2", "=", InterpretationBox[ RowBox[{ RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", SuperscriptBox[ RowBox[{"(", RowBox[{ SuperscriptBox["L1", "2"], "-", SuperscriptBox["L2", "2"]}], ")"}], "2"], " ", SuperscriptBox["\[Pi]", "4"]}], RowBox[{"1080", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "2"]}], RowBox[{"45", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}]], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{"L1", "-", "L2"}], ")"}], " ", RowBox[{"(", RowBox[{"L1", "+", "L2"}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "3"]}], RowBox[{"15", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", SuperscriptBox["L1", "2"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "8"}], "+", "c"}], ")"}], " ", SuperscriptBox["L2", "2"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "4"], " ", SuperscriptBox["q", "4"]}], RowBox[{"15", " ", "c", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 1080] $CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) ($CellContext`L1^2 - $CellContext`L2^2)^2) Pi^4, 0, ((((Rational[ 4, 45] $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-2)) ($CellContext`L1 + $CellContext`L2)) Pi^4, (((( Rational[ 2, 15] $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-2)) ($CellContext`L1 + $CellContext`L2)) Pi^4, (((( Rational[ 4, 15]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-2)) ($CellContext`c $CellContext`L1^2 - (-8 + \ $CellContext`c) $CellContext`L2^2)) Pi^4}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "4"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"2", " ", SuperscriptBox["L1", "6"]}], "-", RowBox[{"3", " ", SuperscriptBox["L1", "4"], " ", SuperscriptBox["L2", "2"]}], "+", SuperscriptBox["L2", "6"]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"]}], RowBox[{"17010", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], "-", SuperscriptBox["L2", "4"]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "2"]}], RowBox[{"945", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "4"], "-", SuperscriptBox["L2", "4"]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "3"]}], RowBox[{"315", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "4"]}]], "+", FractionBox[ RowBox[{"8", " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", SuperscriptBox["L1", "4"]}], "-", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"-", "16"}], "+", "c"}], ")"}], " ", SuperscriptBox["L2", "4"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "6"], " ", SuperscriptBox["q", "4"]}], RowBox[{"315", " ", "c", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "4"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 17010] $CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ( 2 $CellContext`L1^6 - ( 3 $CellContext`L1^4) $CellContext`L2^2 + $CellContext`L2^6)) Pi^6, 0, ((( Rational[ 8, 945] $CellContext`L1^(-6)) $CellContext`L2^(-4)) \ ($CellContext`L1^4 - $CellContext`L2^4)) Pi^6, ((( Rational[ 4, 315] $CellContext`L1^(-6)) $CellContext`L2^(-4)) \ ($CellContext`L1^4 - $CellContext`L2^4)) Pi^6, (((( Rational[ 8, 315]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-4)) ($CellContext`c $CellContext`L1^4 - (-16 + \ $CellContext`c) $CellContext`L2^4)) Pi^6}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "6"]}], "+", RowBox[{ RowBox[{"(", InterpretationBox[ RowBox[{ FractionBox[ RowBox[{"c", " ", RowBox[{"(", RowBox[{ RowBox[{"3", " ", SuperscriptBox["L1", "8"]}], "-", RowBox[{"4", " ", SuperscriptBox["L1", "6"], " ", SuperscriptBox["L2", "2"]}], "+", SuperscriptBox["L2", "8"]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"]}], RowBox[{"226800", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "8"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], "-", SuperscriptBox["L2", "6"]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "2"]}], RowBox[{"4725", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{"2", " ", RowBox[{"(", RowBox[{ SuperscriptBox["L1", "6"], "-", SuperscriptBox["L2", "6"]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "3"]}], RowBox[{"1575", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "6"]}]], "+", FractionBox[ RowBox[{"4", " ", RowBox[{"(", RowBox[{ RowBox[{"c", " ", SuperscriptBox["L1", "6"]}], "+", RowBox[{ RowBox[{"(", RowBox[{"728", "+", RowBox[{"159", " ", "c"}]}], ")"}], " ", SuperscriptBox["L2", "6"]}]}], ")"}], " ", SuperscriptBox["\[Pi]", "8"], " ", SuperscriptBox["q", "4"]}], RowBox[{"1575", " ", "c", " ", SuperscriptBox["L1", "8"], " ", SuperscriptBox["L2", "6"]}]], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "q", "]"}], "5"], SeriesData[$CellContext`q, 0, {}, 0, 5, 1], Editable->False]}], SeriesData[$CellContext`q, 0, {((((Rational[ 1, 226800] $CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) ( 3 $CellContext`L1^8 - ( 4 $CellContext`L1^6) $CellContext`L2^2 + $CellContext`L2^8)) Pi^8, 0, ((( Rational[ 4, 4725] $CellContext`L1^(-8)) $CellContext`L2^(-6)) \ ($CellContext`L1^6 - $CellContext`L2^6)) Pi^8, ((( Rational[ 2, 1575] $CellContext`L1^(-8)) $CellContext`L2^(-6)) \ ($CellContext`L1^6 - $CellContext`L2^6)) Pi^8, (((( Rational[ 4, 1575]/$CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-6)) ($CellContext`c $CellContext`L1^6 + (728 + 159 $CellContext`c) $CellContext`L2^6)) Pi^8}, 0, 5, 1], Editable->False], ")"}], " ", SuperscriptBox["\[ScriptL]", "8"]}], "+", InterpretationBox[ SuperscriptBox[ RowBox[{"O", "[", "\[ScriptL]", "]"}], "10"], SeriesData[$CellContext`\[ScriptL], 0, {}, 4, 10, 1], Editable->False]}], SeriesData[$CellContext`\[ScriptL], 0, { SeriesData[$CellContext`q, 0, {((((Rational[ 1, 1080] $CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-4)) ($CellContext`L1^2 - $CellContext`L2^2)^2) Pi^4, 0, ((((Rational[ 4, 45] $CellContext`L1^(-4)) ($CellContext`L1 - $CellContext`L2)) \ $CellContext`L2^(-2)) ($CellContext`L1 + $CellContext`L2)) Pi^4, (((( Rational[ 2, 15] $CellContext`L1^(-4)) ($CellContext`L1 - \ $CellContext`L2)) $CellContext`L2^(-2)) ($CellContext`L1 + $CellContext`L2)) Pi^4, (((( Rational[ 4, 15]/$CellContext`c) $CellContext`L1^(-4)) \ $CellContext`L2^(-2)) ($CellContext`c $CellContext`L1^2 - (-8 + \ $CellContext`c) $CellContext`L2^2)) Pi^4}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((Rational[ 1, 17010] $CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-6)) ( 2 $CellContext`L1^6 - ( 3 $CellContext`L1^4) $CellContext`L2^2 + $CellContext`L2^6)) Pi^6, 0, (((Rational[ 8, 945] $CellContext`L1^(-6)) $CellContext`L2^(-4)) \ ($CellContext`L1^4 - $CellContext`L2^4)) Pi^6, ((( Rational[ 4, 315] $CellContext`L1^(-6)) $CellContext`L2^(-4)) \ ($CellContext`L1^4 - $CellContext`L2^4)) Pi^6, (((( Rational[ 8, 315]/$CellContext`c) $CellContext`L1^(-6)) \ $CellContext`L2^(-4)) ($CellContext`c $CellContext`L1^4 - (-16 + \ $CellContext`c) $CellContext`L2^4)) Pi^6}, 0, 5, 1], 0, SeriesData[$CellContext`q, 0, {((((Rational[ 1, 226800] $CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-8)) ( 3 $CellContext`L1^8 - ( 4 $CellContext`L1^6) $CellContext`L2^2 + $CellContext`L2^8)) Pi^8, 0, (((Rational[ 4, 4725] $CellContext`L1^(-8)) $CellContext`L2^(-6)) \ ($CellContext`L1^6 - $CellContext`L2^6)) Pi^8, ((( Rational[ 2, 1575] $CellContext`L1^(-8)) $CellContext`L2^(-6)) \ ($CellContext`L1^6 - $CellContext`L2^6)) Pi^8, (((( Rational[ 4, 1575]/$CellContext`c) $CellContext`L1^(-8)) \ $CellContext`L2^(-6)) ($CellContext`c $CellContext`L1^6 + (728 + 159 $CellContext`c) $CellContext`L2^6)) Pi^8}, 0, 5, 1]}, 4, 10, 1], Editable->False]}], ";"}]], "Input", CellChangeTimes->{{3.7041177096676693`*^9, 3.704117722947776*^9}, { 3.7041683208016844`*^9, 3.7041683255367837`*^9}, {3.704189288931673*^9, 3.704189306229148*^9}}] }, Closed]] }, Open ]] }, WindowSize->{1280, 637}, WindowMargins->{{-8, Automatic}, {Automatic, -8}}, FrontEndVersion->"10.3 for Microsoft Windows (64-bit) (October 9, 2015)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[CellGroupData[{ Cell[580, 22, 369, 4, 63, "Section"], Cell[CellGroupData[{ Cell[974, 30, 119, 1, 43, "Subsection"], Cell[1096, 33, 7749, 219, 211, "Input"], Cell[8848, 254, 4432, 117, 80, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[13317, 376, 160, 2, 35, "Subsection"], Cell[13480, 380, 189, 4, 31, "Input"], Cell[13672, 386, 12793, 331, 154, "Input"], Cell[26468, 719, 12810, 315, 247, "Input"], Cell[39281, 1036, 5062, 130, 105, "Input"], Cell[44346, 1168, 8490, 221, 102, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[52885, 1395, 293, 4, 63, "Section"], Cell[CellGroupData[{ Cell[53203, 1403, 211, 2, 43, "Subsection"], Cell[53417, 1407, 8828, 217, 160, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[62282, 1629, 256, 3, 35, "Subsection"], Cell[62541, 1634, 20452, 505, 522, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[83030, 2144, 306, 4, 35, "Subsection"], Cell[83339, 2150, 19181, 472, 376, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[102557, 2627, 351, 4, 35, "Subsection"], Cell[102911, 2633, 19239, 488, 398, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[122199, 3127, 503, 6, 63, "Section"], Cell[CellGroupData[{ Cell[122727, 3137, 236, 3, 43, "Subsection"], Cell[122966, 3142, 11854, 275, 204, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[134857, 3422, 279, 3, 35, "Subsection"], Cell[135139, 3427, 36580, 818, 682, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[171756, 4250, 376, 5, 35, "Subsection"], Cell[172135, 4257, 29419, 685, 556, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[201603, 4948, 429, 5, 63, "Section"], Cell[CellGroupData[{ Cell[202057, 4957, 284, 3, 43, "Subsection"], Cell[202344, 4962, 9577, 229, 202, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[211958, 5196, 335, 4, 35, "Subsection"], Cell[212296, 5202, 31480, 711, 528, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[243813, 5918, 426, 5, 35, "Subsection"], Cell[244242, 5925, 31696, 727, 587, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[275987, 6658, 476, 6, 63, "Section"], Cell[CellGroupData[{ Cell[276488, 6668, 335, 4, 43, "Subsection"], Cell[276826, 6674, 21539, 497, 361, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[298402, 7176, 356, 4, 35, "Subsection"], Cell[298761, 7182, 41039, 931, 615, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[339837, 8118, 453, 6, 35, "Subsection"], Cell[340293, 8126, 32433, 747, 540, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[372775, 8879, 593, 8, 63, "Section"], Cell[CellGroupData[{ Cell[373393, 8891, 391, 5, 43, "Subsection"], Cell[373787, 8898, 14544, 342, 364, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[388368, 9245, 414, 5, 35, "Subsection"], Cell[388785, 9252, 49778, 1084, 926, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[438600, 10341, 505, 6, 35, "Subsection"], Cell[439108, 10349, 51614, 1145, 843, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[490771, 11500, 616, 8, 63, "Section"], Cell[CellGroupData[{ Cell[491412, 11512, 391, 5, 43, "Subsection"], Cell[491806, 11519, 1836, 49, 56, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[493679, 11573, 466, 6, 35, "Subsection"], Cell[494148, 11581, 8105, 193, 199, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[502290, 11779, 502, 6, 35, "Subsection"], Cell[502795, 11787, 8489, 204, 197, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[511333, 11997, 609, 8, 63, "Section"], Cell[CellGroupData[{ Cell[511967, 12009, 166, 2, 43, "Subsection"], Cell[512136, 12013, 8063, 201, 167, InheritFromParent] }, Closed]], Cell[CellGroupData[{ Cell[520236, 12219, 228, 3, 35, "Subsection"], Cell[520467, 12224, 1371, 36, 56, InheritFromParent] }, Closed]], Cell[CellGroupData[{ Cell[521875, 12265, 147, 1, 35, "Subsection"], Cell[522025, 12268, 1219, 31, 52, InheritFromParent] }, Closed]], Cell[CellGroupData[{ Cell[523281, 12304, 221, 2, 35, "Subsection"], Cell[523505, 12308, 1217, 31, 52, InheritFromParent] }, Closed]], Cell[CellGroupData[{ Cell[524759, 12344, 284, 4, 35, "Subsection"], Cell[525046, 12350, 1214, 31, 52, InheritFromParent] }, Closed]], Cell[CellGroupData[{ Cell[526297, 12386, 366, 5, 35, "Subsection"], Cell[526666, 12393, 1323, 34, 52, InheritFromParent] }, Closed]], Cell[CellGroupData[{ Cell[528026, 12432, 434, 6, 35, "Subsection"], Cell[528463, 12440, 2842, 73, 57, InheritFromParent] }, Closed]], Cell[CellGroupData[{ Cell[531342, 12518, 382, 5, 35, "Subsection"], Cell[531727, 12525, 1217, 31, 52, InheritFromParent] }, Closed]], Cell[CellGroupData[{ Cell[532981, 12561, 575, 8, 35, "Subsection"], Cell[533559, 12571, 1671, 43, 53, "Input"] }, Closed]] }, Open ]], Cell[CellGroupData[{ Cell[535279, 12620, 369, 4, 63, "Section"], Cell[CellGroupData[{ Cell[535673, 12628, 254, 3, 43, "Subsection"], Cell[535930, 12633, 5441, 139, 109, "Input"] }, Closed]], Cell[CellGroupData[{ Cell[541408, 12777, 396, 5, 35, "Subsection"], Cell[541807, 12784, 12017, 308, 150, "Input"] }, Closed]] }, Open ]] } ] *) (* End of internal cache information *)