(* ::Package:: *) (* -------------------------------- *) (* -------- Ancillary File -------- *) (* -------------------------------- *) (* Loading this file in a Mathematica session with Get["path/ancillary_file.txt"] sets several symbols with the results of the threshold, Regge and high energy expansion of the amplitude. *) (* See the Print command below for further details *) Print["Ancillary file The file contains the threshold, Regge and high energy expansions of the amplitude. With loading this file, the following symbols are set: {M[TE], M[RE], r0, r1, j0, j1, M[HE]}. The symbols are explained below, including the definitions of the variables used in the respective expansions. - Threshold Expansion; see eq. (2.14) Variables: b = beta_u, ggb = g^2/beta_u M[TE] gives the leading, sub-leading and sub-sub-leading term of (m^2 Im[M])/(-Pi g^2 t) in the threshold expansion with beta_u as the expansion parameter. - Regge Expansion; see eq. (3.5) Variables: Y = (beta_uv - beta_v)/(beta_uv + beta_u) , x = (beta_v - 1)/(beta_v + 1), xi = (1-x)/(1+x) M[RE] gives the sub-sub-leading term in the Regge expansion (proportional to Y^2) of M(1+Y)/(1-Y). jo and j1 give the leading and sub-leading Regge trajectories, respectively. ro and r1 give the leading and sub-leading residues, respectively. - High Energy Expansion; see eq. (2.15) Variables: R = u/v, rho = (u+v)/4, t = v/(u+v) M[HE] gives the leading and the first sub-leading term of the amplitude M with rho as the expansion parameter. "] (* -------------------------------- *) (* ----- Threshold Expansion ------ *) (* -------------------------------- *) (* Variables: b = beta_u, ggb = g^2/beta_u *) M[TE]=( b*(1 + 2*ggb*Pi^2 + (4*ggb^2*Pi^4)/3) + b^2*(ggb*(-32 + 16*ggb) + ggb^2*(48*ggb*Pi^2 + 16*Pi^2*(-3 + Log[2]))) + b^3*(t/(6*m^2) + (ggb*Pi^2*t)/(3*m^2) + ggb^2*(416 + 128*ggb^2 + (64*ggb*(-21 + Pi^2))/3 + (2*Pi^2*(((3 + Pi^2)*t)/m^2 + 36*(-7 + Log[4])))/9 + 168*Zeta[3])) ); (* -------------------------------- *) (* ------- Regge Expansion -------- *) (* -------------------------------- *) (* Variables: Y = (beta_uv - beta_v)/(beta_uv + beta_u) , x = (beta_v - 1)/(beta_v + 1), xi = (1-x)/(1+x) *) (* --- Regge trajectories j0, j1 and residues r0, r1 --- *) j0=( -1 - g^2*xi*HPL[{1}, 1 - x^2] + g^4*(xi^2*(-2*HPL[{1, 2}, 1 - x^2] - HPL[{1, 1, 1}, 1 - x^2]) + xi*((2*Pi^2*HPL[{1}, 1 - x^2])/3 + HPL[{1, 1, 1}, 1 - x^2])) + g^6*(xi^3*(-8*HPL[{1, 1, 3}, 1 - x^2] - 8*HPL[{1, 2, 2}, 1 - x^2] - 8*HPL[{1, 1, 1, 2}, 1 - x^2] - 4*HPL[{1, 1, 2, 1}, 1 - x^2] - 4*HPL[{1, 2, 1, 1}, 1 - x^2] - 6*HPL[{1, 1, 1, 1, 1}, 1 - x^2]) + xi*((-2*Pi^4*HPL[{1}, 1 - x^2])/3 - 2*Pi^2*HPL[{1, 1, 1}, 1 - x^2] - 5*HPL[{1, 1, 1, 1, 1}, 1 - x^2]) + xi^2*((4*Pi^2*HPL[{1, 2}, 1 - x^2])/3 + (8*Pi^2*HPL[{2, 1}, 1 - x^2])/3 + 2*Pi^2*HPL[{1, 1, 1}, 1 - x^2] + 8*HPL[{1, 1, 1, 2}, 1 - x^2] + 6*HPL[{1, 2, 1, 1}, 1 - x^2] + 8*HPL[{2, 1, 1, 1}, 1 - x^2] + 11*HPL[{1, 1, 1, 1, 1}, 1 - x^2] + 12*HPL[{1, 1}, 1 - x^2]*Zeta[3])) ); j1=( -2 - 4*g^2 + g^4*(16 + (8*Pi^2)/3 - 8*xi*HPL[{1}, 1 - x^2] + 4*HPL[{1, 1}, 1 - x^2] + ((-2*Pi^2*HPL[{1}, 1 - x^2])/3 - HPL[{1, 1, 1}, 1 - x^2])/xi) + g^6*(-128 - (32*Pi^2)/3 - (8*Pi^4)/3 - 24*HPL[{1, 1}, 1 - x^2] - 8*Pi^2*HPL[{1, 1}, 1 - x^2] - 16*xi^2*HPL[{1, 1}, 1 - x^2] + 32*HPL[{1, 2}, 1 - x^2] + 16*HPL[{1, 1, 1}, 1 - x^2] + xi*(96*HPL[{1}, 1 - x^2] + 8*Pi^2*HPL[{1}, 1 - x^2] - 64*HPL[{2}, 1 - x^2] - 32*HPL[{1, 1}, 1 - x^2] + 28*HPL[{1, 1, 1}, 1 - x^2]) - 20*HPL[{1, 1, 1, 1}, 1 - x^2] + 96*Zeta[3] + ((8*Pi^2*HPL[{1}, 1 - x^2])/3 + (44*Pi^4*HPL[{1}, 1 - x^2])/45 + 4*HPL[{1, 1, 1}, 1 - x^2] + (8*Pi^2*HPL[{1, 1, 1}, 1 - x^2])/3 - 8*HPL[{1, 1, 2}, 1 - x^2] - 4*HPL[{1, 1, 1, 1}, 1 - x^2] + 6*HPL[{1, 1, 1, 1, 1}, 1 - x^2] - 24*HPL[{1}, 1 - x^2]*Zeta[3])/xi) ); r0=( 1 + g^2*xi*(Pi^2 - 4*HPL[{-2}, x] - 4*HPL[{2}, x]) + g^4*(xi^2*((2*Pi^4)/3 - 16*HPL[{-4}, x] - 8*Pi^2*HPL[{-2}, x] - 16*HPL[{4}, x] + 32*HPL[{-3, -1}, x] + 32*HPL[{-3, 1}, x] + 32*HPL[{-2, -2}, x] + 32*HPL[{-2, 2}, x] + 4*Pi^2*HPL[{0, 0}, x] + 32*HPL[{3, -1}, x] + 32*HPL[{3, 1}, x] + 8*HPL[{0, 0, 0, 0}, x]) + xi*((-7*Pi^4)/15 + 16*HPL[{-4}, x] + (8*Pi^2*HPL[{-2}, x])/3 + (8*Pi^2*HPL[{2}, x])/3 + 16*HPL[{4}, x] + (8*Pi^2*HPL[{-1, 0}, x])/3 - 4*Pi^2*HPL[{0, 0}, x] + (8*Pi^2*HPL[{1, 0}, x])/3 + 16*HPL[{-2, 0, 0}, x] + 16*HPL[{-1, 0, 0, 0}, x] - 8*HPL[{0, 0, 0, 0}, x] + 16*HPL[{1, 0, 0, 0}, x] - 4*HPL[{0}, x]*Zeta[3])) + g^6*(xi^2*((-188*Pi^6)/315 + 864*HPL[{-6}, x] + 160*Pi^2*HPL[{-4}, x] + (368*Pi^4*HPL[{-2}, x])/45 + (88*Pi^4*HPL[{2}, x])/45 + 32*Pi^2*HPL[{4}, x] + 864*HPL[{6}, x] - 512*HPL[{-5, -1}, x] + 768*HPL[{-5, 0}, x] - 512*HPL[{-5, 1}, x] - 512*HPL[{-4, -2}, x] - 512*HPL[{-4, 2}, x] - 256*HPL[{-3, -3}, x] - (128*Pi^2*HPL[{-3, -1}, x])/3 + (224*Pi^2*HPL[{-3, 0}, x])/3 - (128*Pi^2*HPL[{-3, 1}, x])/3 - 256*HPL[{-3, 3}, x] - 512*HPL[{-2, -4}, x] - (128*Pi^2*HPL[{-2, -2}, x])/3 - (128*Pi^2*HPL[{-2, 2}, x])/3 - 512*HPL[{-2, 4}, x] - 512*HPL[{-1, -5}, x] - (128*Pi^2*HPL[{-1, -3}, x])/3 + (352*Pi^4*HPL[{-1, 0}, x])/45 - (128*Pi^2*HPL[{-1, 3}, x])/3 - 512*HPL[{-1, 5}, x] - (652*Pi^4*HPL[{0, 0}, x])/45 + 64*HPL[{2, -4}, x] - (64*Pi^2*HPL[{2, -2}, x])/3 - (64*Pi^2*HPL[{2, 2}, x])/3 + 64*HPL[{2, 4}, x] - 128*HPL[{3, -3}, x] - (128*Pi^2*HPL[{3, -1}, x])/3 + (112*Pi^2*HPL[{3, 0}, x])/3 - (128*Pi^2*HPL[{3, 1}, x])/3 - 128*HPL[{3, 3}, x] - 512*HPL[{5, -1}, x] - 512*HPL[{5, 1}, x] + 608*HPL[{-4, 0, 0}, x] - 256*HPL[{-3, -2, 0}, x] - 512*HPL[{-2, -3, 0}, x] - (128*Pi^2*HPL[{-2, -1, 0}, x])/3 + 96*Pi^2*HPL[{-2, 0, 0}, x] - (64*Pi^2*HPL[{-2, 1, 0}, x])/3 - 768*HPL[{-1, -4, 0}, x] - (128*Pi^2*HPL[{-1, -2, 0}, x])/3 - (64*Pi^2*HPL[{2, -1, 0}, x])/3 - (32*Pi^2*HPL[{2, 0, 0}, x])/3 - (32*Pi^2*HPL[{2, 1, 0}, x])/3 - 80*HPL[{4, 0, 0}, x] - 256*HPL[{-3, -1, 0, 0}, x] + 384*HPL[{-3, 0, 0, 0}, x] - 128*HPL[{-3, 1, 0, 0}, x] - 512*HPL[{-2, -2, 0, 0}, x] + 64*HPL[{-2, 2, 0, 0}, x] - 512*HPL[{-1, -3, 0, 0}, x] + (256*Pi^2*HPL[{-1, 0, 0, 0}, x])/3 - (512*Pi^2*HPL[{0, 0, 0, 0}, x])/3 + 64*HPL[{2, -2, 0, 0}, x] - 160*HPL[{2, 2, 0, 0}, x] - 128*HPL[{3, -1, 0, 0}, x] + 64*HPL[{3, 0, 0, 0}, x] - 64*HPL[{3, 1, 0, 0}, x] - 256*HPL[{-2, -1, 0, 0, 0}, x] + 608*HPL[{-2, 0, 0, 0, 0}, x] - 128*HPL[{-2, 1, 0, 0, 0}, x] - 256*HPL[{-1, -2, 0, 0, 0}, x] - 128*HPL[{2, -1, 0, 0, 0}, x] - 80*HPL[{2, 0, 0, 0, 0}, x] - 64*HPL[{2, 1, 0, 0, 0}, x] + 768*HPL[{-1, 0, 0, 0, 0, 0}, x] - 1032*HPL[{0, 0, 0, 0, 0, 0}, x] + (32*Pi^2*HPL[{-1}, x]*Zeta[3])/3 - 16*Pi^2*HPL[{0}, x]*Zeta[3] + 64*HPL[{-2, 0}, x]*Zeta[3] - 64*HPL[{2, 0}, x]*Zeta[3] - 64*HPL[{0, 0, 0}, x]*Zeta[3] - 16*Zeta[3]^2 + 32*HPL[{-1}, x]*Zeta[5] - 32*HPL[{0}, x]*Zeta[5]) + xi^3*((17*Pi^6)/45 - 544*HPL[{-6}, x] - 128*Pi^2*HPL[{-4}, x] - 8*Pi^4*HPL[{-2}, x] + (8*Pi^4*HPL[{2}, x])/3 - 544*HPL[{6}, x] + 512*HPL[{-5, -1}, x] - 512*HPL[{-5, 0}, x] + 512*HPL[{-5, 1}, x] + 512*HPL[{-4, -2}, x] + 512*HPL[{-4, 2}, x] + 256*HPL[{-3, -3}, x] + 128*Pi^2*HPL[{-3, -1}, x] - 64*Pi^2*HPL[{-3, 0}, x] + 256*HPL[{-3, 3}, x] + 192*HPL[{-2, -4}, x] + 96*Pi^2*HPL[{-2, -2}, x] + 192*HPL[{-2, 4}, x] + (352*Pi^4*HPL[{0, 0}, x])/45 - 64*HPL[{2, -4}, x] - 32*Pi^2*HPL[{2, -2}, x] - 64*HPL[{2, 4}, x] + 512*HPL[{5, -1}, x] + 512*HPL[{5, 1}, x] - 384*HPL[{-4, -1, -1}, x] - 384*HPL[{-4, -1, 1}, x] - 288*HPL[{-4, 0, 0}, x] - 384*HPL[{-4, 1, -1}, x] - 384*HPL[{-4, 1, 1}, x] - 512*HPL[{-3, -2, -1}, x] - 512*HPL[{-3, -2, 1}, x] - 512*HPL[{-3, -1, -2}, x] - 512*HPL[{-3, -1, 2}, x] - 512*HPL[{-3, 2, -1}, x] - 512*HPL[{-3, 2, 1}, x] - 384*HPL[{-2, -3, -1}, x] - 384*HPL[{-2, -3, 1}, x] - 384*HPL[{-2, -2, -2}, x] - 384*HPL[{-2, -2, 2}, x] - 48*Pi^2*HPL[{-2, 0, 0}, x] - 384*HPL[{-2, 3, -1}, x] - 384*HPL[{-2, 3, 1}, x] + 128*HPL[{2, -3, -1}, x] + 128*HPL[{2, -3, 1}, x] + 128*HPL[{2, -2, -2}, x] + 128*HPL[{2, -2, 2}, x] + 16*Pi^2*HPL[{2, 0, 0}, x] + 128*HPL[{2, 3, -1}, x] + 128*HPL[{2, 3, 1}, x] - 384*HPL[{4, -1, -1}, x] - 384*HPL[{4, -1, 1}, x] + 32*HPL[{4, 0, 0}, x] - 384*HPL[{4, 1, -1}, x] - 384*HPL[{4, 1, 1}, x] - 128*HPL[{-3, 0, 0, 0}, x] + (280*Pi^2*HPL[{0, 0, 0, 0}, x])/3 - 96*HPL[{-2, 0, 0, 0, 0}, x] + 32*HPL[{2, 0, 0, 0, 0}, x] + 544*HPL[{0, 0, 0, 0, 0, 0}, x] + 8*Pi^2*HPL[{0}, x]*Zeta[3] + 16*HPL[{0, 0, 0}, x]*Zeta[3] + 16*HPL[{0}, x]*Zeta[5]) + xi*((262*Pi^6)/945 - 320*HPL[{-6}, x] - 32*Pi^2*HPL[{-4}, x] - (8*Pi^4*HPL[{-2}, x])/3 - (8*Pi^4*HPL[{2}, x])/3 - 32*Pi^2*HPL[{4}, x] - 320*HPL[{6}, x] - 256*HPL[{-5, 0}, x] - 32*Pi^2*HPL[{-3, 0}, x] - (8*Pi^4*HPL[{-1, 0}, x])/3 + (20*Pi^4*HPL[{0, 0}, x])/3 - (8*Pi^4*HPL[{1, 0}, x])/3 - 16*Pi^2*HPL[{3, 0}, x] - 320*HPL[{-4, 0, 0}, x] - 32*Pi^2*HPL[{-2, 0, 0}, x] - (32*Pi^2*HPL[{2, 0, 0}, x])/3 + 48*HPL[{4, 0, 0}, x] - 192*HPL[{-3, 0, 0, 0}, x] - 32*Pi^2*HPL[{-1, 0, 0, 0}, x] + (232*Pi^2*HPL[{0, 0, 0, 0}, x])/3 - 32*Pi^2*HPL[{1, 0, 0, 0}, x] - 96*HPL[{3, 0, 0, 0}, x] - 320*HPL[{-2, 0, 0, 0, 0}, x] - 64*HPL[{2, 0, 0, 0, 0}, x] - 320*HPL[{-1, 0, 0, 0, 0, 0}, x] + 488*HPL[{0, 0, 0, 0, 0, 0}, x] - 320*HPL[{1, 0, 0, 0, 0, 0}, x] + (8*Pi^2*HPL[{0}, x]*Zeta[3])/3 + 48*HPL[{0, 0, 0}, x]*Zeta[3] + 52*HPL[{0}, x]*Zeta[5])) ); r1=( 2 + g^2*(-8 + 16*HPL[{-1}, x] + 16*HPL[{1}, x]) + g^4*(96 - 64*HPL[{-3}, x] - 128*HPL[{-1}, x] - (32*Pi^2*HPL[{-1}, x])/3 + 16*Pi^2*HPL[{0}, x] - 128*HPL[{1}, x] - (32*Pi^2*HPL[{1}, x])/3 - 64*HPL[{3}, x] + 128*HPL[{-1, -1}, x] + 128*HPL[{-1, 1}, x] + 32*HPL[{0, 0}, x] + 16*xi^2*HPL[{0, 0}, x] + 128*HPL[{1, -1}, x] + 128*HPL[{1, 1}, x] - 64*HPL[{-1, 0, 0}, x] + 32*HPL[{0, 0, 0}, x] + xi*(16*Pi^2 - 64*HPL[{-2}, x] + 64*HPL[{0}, x] + (8*Pi^2*HPL[{0}, x])/3 - 64*HPL[{2}, x] + 16*HPL[{0, 0, 0}, x]) + 16*Zeta[3] + ((14*Pi^4)/15 - 32*HPL[{-4}, x] - (16*Pi^2*HPL[{-2}, x])/3 - (8*Pi^2*HPL[{0}, x])/3 - (16*Pi^2*HPL[{2}, x])/3 - 32*HPL[{4}, x] - (16*Pi^2*HPL[{-1, 0}, x])/3 + 8*Pi^2*HPL[{0, 0}, x] - (16*Pi^2*HPL[{1, 0}, x])/3 - 32*HPL[{-2, 0, 0}, x] - 16*HPL[{0, 0, 0}, x] - 32*HPL[{-1, 0, 0, 0}, x] + 16*HPL[{0, 0, 0, 0}, x] - 32*HPL[{1, 0, 0, 0}, x] + 8*HPL[{0}, x]*Zeta[3])/xi) + g^6*(-1280 - (128*Pi^4)/15 + 1280*HPL[{-5}, x] + 768*HPL[{-4}, x] + 896*HPL[{-3}, x] + 128*Pi^2*HPL[{-3}, x] + 256*Pi^2*HPL[{-2}, x] + 1536*HPL[{-1}, x] + (256*Pi^2*HPL[{-1}, x])/3 + (32*Pi^4*HPL[{-1}, x])/3 - (416*Pi^2*HPL[{0}, x])/3 - (80*Pi^4*HPL[{0}, x])/3 + 1536*HPL[{1}, x] + (256*Pi^2*HPL[{1}, x])/3 + (32*Pi^4*HPL[{1}, x])/3 + 896*HPL[{3}, x] + 128*Pi^2*HPL[{3}, x] + 768*HPL[{4}, x] + 1280*HPL[{5}, x] + 1024*HPL[{-4, 0}, x] - 1024*HPL[{-3, -1}, x] + 512*HPL[{-3, 0}, x] - 1024*HPL[{-3, 1}, x] - 1024*HPL[{-2, -2}, x] + 1024*HPL[{-2, 0}, x] + 128*Pi^2*HPL[{-2, 0}, x] - 1024*HPL[{-2, 2}, x] - 1024*HPL[{-1, -3}, x] - 1536*HPL[{-1, -1}, x] - (512*Pi^2*HPL[{-1, -1}, x])/3 + (512*Pi^2*HPL[{-1, 0}, x])/3 - 1536*HPL[{-1, 1}, x] - (512*Pi^2*HPL[{-1, 1}, x])/3 - 1024*HPL[{-1, 3}, x] - 576*HPL[{0, 0}, x] - (512*Pi^2*HPL[{0, 0}, x])/3 - 512*HPL[{1, -3}, x] - 1536*HPL[{1, -1}, x] - (512*Pi^2*HPL[{1, -1}, x])/3 + 128*Pi^2*HPL[{1, 0}, x] - 1536*HPL[{1, 1}, x] - (512*Pi^2*HPL[{1, 1}, x])/3 - 512*HPL[{1, 3}, x] + 64*Pi^2*HPL[{2, 0}, x] - 1024*HPL[{3, -1}, x] - 1024*HPL[{3, 1}, x] + 1280*HPL[{-3, 0, 0}, x] + 256*HPL[{-2, 0, 0}, x] - 1024*HPL[{-1, -2, 0}, x] + 1024*HPL[{-1, -1, -1}, x] + 1024*HPL[{-1, -1, 1}, x] + 896*HPL[{-1, 0, 0}, x] + 128*Pi^2*HPL[{-1, 0, 0}, x] + 1024*HPL[{-1, 1, -1}, x] + 1024*HPL[{-1, 1, 1}, x] - 768*HPL[{0, 0, 0}, x] - (928*Pi^2*HPL[{0, 0, 0}, x])/3 + 1024*HPL[{1, -1, -1}, x] + 1024*HPL[{1, -1, 1}, x] + 384*HPL[{1, 0, 0}, x] + (128*Pi^2*HPL[{1, 0, 0}, x])/3 + 1024*HPL[{1, 1, -1}, x] + 1024*HPL[{1, 1, 1}, x] + 128*HPL[{2, 0, 0}, x] - 192*HPL[{3, 0, 0}, x] + 768*HPL[{-2, 0, 0, 0}, x] - 1024*HPL[{-1, -1, 0, 0}, x] + 768*HPL[{-1, 0, 0, 0}, x] - 512*HPL[{-1, 1, 0, 0}, x] - 960*HPL[{0, 0, 0, 0}, x] - 512*HPL[{1, -1, 0, 0}, x] + 128*HPL[{1, 0, 0, 0}, x] - 256*HPL[{1, 1, 0, 0}, x] + 384*HPL[{2, 0, 0, 0}, x] + 1280*HPL[{-1, 0, 0, 0, 0}, x] - 1952*HPL[{0, 0, 0, 0, 0}, x] + 256*HPL[{1, 0, 0, 0, 0}, x] + xi^2*(384*HPL[{-3}, x] - (160*Pi^2*HPL[{0}, x])/3 + 384*HPL[{3}, x] + 512*HPL[{-2, 0}, x] - 576*HPL[{0, 0}, x] - (64*Pi^2*HPL[{0, 0}, x])/3 + 384*HPL[{-1, 0, 0}, x] - 512*HPL[{0, 0, 0}, x] - 128*HPL[{1, 0, 0}, x] - 256*HPL[{0, 0, 0, 0}, x] - 64*Zeta[3]) - 64*Zeta[3] - (32*Pi^2*Zeta[3])/3 - 192*HPL[{0, 0}, x]*Zeta[3] + xi*(-256*Pi^2 - (736*Pi^4)/45 + 1024*HPL[{-4}, x] + 512*HPL[{-3}, x] + 1536*HPL[{-2}, x] + (256*Pi^2*HPL[{-2}, x])/3 + 256*Pi^2*HPL[{-1}, x] - 1536*HPL[{0}, x] - (512*Pi^2*HPL[{0}, x])/3 - (8*Pi^4*HPL[{0}, x])/3 + 1536*HPL[{2}, x] + (256*Pi^2*HPL[{2}, x])/3 + 512*HPL[{3}, x] + 1024*HPL[{4}, x] + 1024*HPL[{-3, 0}, x] - 1024*HPL[{-2, -1}, x] - 1024*HPL[{-2, 1}, x] - 1024*HPL[{-1, -2}, x] + 1536*HPL[{-1, 0}, x] + (256*Pi^2*HPL[{-1, 0}, x])/3 - 1024*HPL[{-1, 2}, x] - 768*HPL[{0, 0}, x] - 192*Pi^2*HPL[{0, 0}, x] + (128*Pi^2*HPL[{1, 0}, x])/3 - 1024*HPL[{2, -1}, x] - 1024*HPL[{2, 1}, x] + 1024*HPL[{-2, 0, 0}, x] - 1024*HPL[{0, 0, 0}, x] - 32*Pi^2*HPL[{0, 0, 0}, x] - 128*HPL[{2, 0, 0}, x] + 512*HPL[{-1, 0, 0, 0}, x] - 1216*HPL[{0, 0, 0, 0}, x] + 256*HPL[{1, 0, 0, 0}, x] - 320*HPL[{0, 0, 0, 0, 0}, x] - 128*HPL[{0}, x]*Zeta[3]) - 208*Zeta[5] + ((-56*Pi^4)/15 - (232*Pi^6)/189 + 768*HPL[{-6}, x] + 384*HPL[{-5}, x] + 128*HPL[{-4}, x] + (256*Pi^2*HPL[{-4}, x])/3 + 128*Pi^2*HPL[{-3}, x] + (64*Pi^2*HPL[{-2}, x])/3 + (352*Pi^4*HPL[{-2}, x])/45 + (128*Pi^4*HPL[{-1}, x])/15 - (8*Pi^4*HPL[{0}, x])/5 + (128*Pi^4*HPL[{1}, x])/15 + (64*Pi^2*HPL[{2}, x])/3 + (352*Pi^4*HPL[{2}, x])/45 + 128*HPL[{4}, x] + (256*Pi^2*HPL[{4}, x])/3 + 384*HPL[{5}, x] + 768*HPL[{6}, x] + 512*HPL[{-5, 0}, x] - 512*HPL[{-4, -1}, x] + 256*HPL[{-4, 0}, x] - 512*HPL[{-4, 1}, x] - 512*HPL[{-3, -2}, x] + (256*Pi^2*HPL[{-3, 0}, x])/3 - 512*HPL[{-3, 2}, x] - 512*HPL[{-2, -3}, x] - (256*Pi^2*HPL[{-2, -1}, x])/3 + (256*Pi^2*HPL[{-2, 0}, x])/3 - (256*Pi^2*HPL[{-2, 1}, x])/3 - 512*HPL[{-2, 3}, x] - 512*HPL[{-1, -4}, x] - (256*Pi^2*HPL[{-1, -2}, x])/3 + (64*Pi^2*HPL[{-1, 0}, x])/3 + (352*Pi^4*HPL[{-1, 0}, x])/45 - (256*Pi^2*HPL[{-1, 2}, x])/3 - 512*HPL[{-1, 4}, x] - 32*Pi^2*HPL[{0, 0}, x] - (832*Pi^4*HPL[{0, 0}, x])/45 - 512*HPL[{1, -4}, x] - (256*Pi^2*HPL[{1, -2}, x])/3 + (64*Pi^2*HPL[{1, 0}, x])/3 + (352*Pi^4*HPL[{1, 0}, x])/45 - (256*Pi^2*HPL[{1, 2}, x])/3 - 512*HPL[{1, 4}, x] - 256*HPL[{2, -3}, x] - (256*Pi^2*HPL[{2, -1}, x])/3 + 64*Pi^2*HPL[{2, 0}, x] - (256*Pi^2*HPL[{2, 1}, x])/3 - 256*HPL[{2, 3}, x] + (128*Pi^2*HPL[{3, 0}, x])/3 - 512*HPL[{4, -1}, x] - 512*HPL[{4, 1}, x] + 768*HPL[{-4, 0, 0}, x] + 128*HPL[{-3, 0, 0}, x] - 512*HPL[{-2, -2, 0}, x] + 128*HPL[{-2, 0, 0}, x] + (256*Pi^2*HPL[{-2, 0, 0}, x])/3 - 512*HPL[{-1, -3, 0}, x] - (256*Pi^2*HPL[{-1, -1, 0}, x])/3 + (256*Pi^2*HPL[{-1, 0, 0}, x])/3 - (256*Pi^2*HPL[{-1, 1, 0}, x])/3 - 32*Pi^2*HPL[{0, 0, 0}, x] - 512*HPL[{1, -3, 0}, x] - (256*Pi^2*HPL[{1, -1, 0}, x])/3 + (256*Pi^2*HPL[{1, 0, 0}, x])/3 - (256*Pi^2*HPL[{1, 1, 0}, x])/3 + (128*Pi^2*HPL[{2, 0, 0}, x])/3 + 64*HPL[{3, 0, 0}, x] - 128*HPL[{4, 0, 0}, x] + 512*HPL[{-3, 0, 0, 0}, x] - 512*HPL[{-2, -1, 0, 0}, x] + 384*HPL[{-2, 0, 0, 0}, x] - 256*HPL[{-2, 1, 0, 0}, x] - 512*HPL[{-1, -2, 0, 0}, x] + 128*HPL[{-1, 0, 0, 0}, x] + (256*Pi^2*HPL[{-1, 0, 0, 0}, x])/3 - 256*HPL[{-1, 2, 0, 0}, x] - 64*HPL[{0, 0, 0, 0}, x] - 192*Pi^2*HPL[{0, 0, 0, 0}, x] - 512*HPL[{1, -2, 0, 0}, x] + 128*HPL[{1, 0, 0, 0}, x] + (256*Pi^2*HPL[{1, 0, 0, 0}, x])/3 - 256*HPL[{1, 2, 0, 0}, x] - 256*HPL[{2, -1, 0, 0}, x] + 64*HPL[{2, 0, 0, 0}, x] - 128*HPL[{2, 1, 0, 0}, x] + 256*HPL[{3, 0, 0, 0}, x] + 768*HPL[{-2, 0, 0, 0, 0}, x] - 512*HPL[{-1, -1, 0, 0, 0}, x] + 384*HPL[{-1, 0, 0, 0, 0}, x] - 512*HPL[{-1, 1, 0, 0, 0}, x] + 96*HPL[{0, 0, 0, 0, 0}, x] - 512*HPL[{1, -1, 0, 0, 0}, x] + 384*HPL[{1, 0, 0, 0, 0}, x] - 512*HPL[{1, 1, 0, 0, 0}, x] + 256*HPL[{2, 0, 0, 0, 0}, x] + 768*HPL[{-1, 0, 0, 0, 0, 0}, x] - 1088*HPL[{0, 0, 0, 0, 0, 0}, x] + 768*HPL[{1, 0, 0, 0, 0, 0}, x] + (32*Pi^2*Zeta[3])/3 - 32*HPL[{0}, x]*Zeta[3] - (32*Pi^2*HPL[{0}, x]*Zeta[3])/3 - 128*HPL[{0, 0, 0}, x]*Zeta[3] + 32*Zeta[5] - 112*HPL[{0}, x]*Zeta[5])/xi) ); (* --- Sub-sub-leading term in the Regge expansion (proportional to Y^2) of (1+Y)/(1-Y)*M --- *) M[RE]= Y^2( 2 + g^2*((4*(-1 + xi^2)*(1 + 4*HPL[{-1}, x] + 4*HPL[{1}, x]))/xi^2 + (8 - 8/xi^2)*Log[Y]) + g^4*((-8*(-12*xi*(5 - 6*xi^2 + 2*xi^4)*HPL[{-1}, x] + (6*xi^2*(6 - 6*xi^2 + xi^4) + Pi^2*(3 - 5*xi^2 + 2*xi^4))*HPL[{0}, x] + 2*(15*xi + 3*Pi^2*xi - 3*xi^3 - 4*Pi^2*xi^3 - 3*xi^5 + Pi^2*xi^5 - 6*xi*(5 - 6*xi^2 + 2*xi^4)*HPL[{1}, x] + 6*xi*(3 - 4*xi^2 + xi^4)*HPL[{0, 0}, x] + 9*HPL[{0, 0, 0}, x] - 15*xi^2*HPL[{0, 0, 0}, x] + 6*xi^4*HPL[{0, 0, 0}, x]))*Log[Y])/(3*xi^3*(-1 + xi^2)) + (8*(5 - 6*xi^2 + 2*xi^4)*Log[Y]^2)/(xi^2*(-1 + xi^2)) + (2*(21*Pi^4 + 570*xi - 80*Pi^2*xi + 360*Pi^2*xi^2 - 35*Pi^4*xi^2 + 540*xi^3 + 160*Pi^2*xi^3 - 360*Pi^2*xi^4 + 14*Pi^4*xi^4 - 420*xi^5 - 80*Pi^2*xi^5 + 60*Pi^2*xi^6 - 240*(3 - 5*xi^2 + 2*xi^4)*HPL[{-4}, x] - 480*xi*(3 - 4*xi^2 + xi^4)*HPL[{-3}, x] - 120*Pi^2*HPL[{-2}, x] - 1440*xi^2*HPL[{-2}, x] + 200*Pi^2*xi^2*HPL[{-2}, x] + 1440*xi^4*HPL[{-2}, x] - 80*Pi^2*xi^4*HPL[{-2}, x] - 240*xi^6*HPL[{-2}, x] - 1200*xi*HPL[{-1}, x] - 240*Pi^2*xi*HPL[{-1}, x] + 240*xi^3*HPL[{-1}, x] + 320*Pi^2*xi^3*HPL[{-1}, x] + 240*xi^5*HPL[{-1}, x] - 80*Pi^2*xi^5*HPL[{-1}, x] - 70*Pi^2*HPL[{0}, x] + 360*Pi^2*xi*HPL[{0}, x] + 1320*xi^2*HPL[{0}, x] + 150*Pi^2*xi^2*HPL[{0}, x] - 480*Pi^2*xi^3*HPL[{0}, x] - 1080*xi^4*HPL[{0}, x] - 90*Pi^2*xi^4*HPL[{0}, x] + 120*Pi^2*xi^5*HPL[{0}, x] + 120*xi^6*HPL[{0}, x] + 10*Pi^2*xi^6*HPL[{0}, x] - 1200*xi*HPL[{1}, x] - 240*Pi^2*xi*HPL[{1}, x] + 240*xi^3*HPL[{1}, x] + 320*Pi^2*xi^3*HPL[{1}, x] + 240*xi^5*HPL[{1}, x] - 80*Pi^2*xi^5*HPL[{1}, x] - 120*Pi^2*HPL[{2}, x] - 1440*xi^2*HPL[{2}, x] + 200*Pi^2*xi^2*HPL[{2}, x] + 1440*xi^4*HPL[{2}, x] - 80*Pi^2*xi^4*HPL[{2}, x] - 240*xi^6*HPL[{2}, x] - 1440*xi*HPL[{3}, x] + 1920*xi^3*HPL[{3}, x] - 480*xi^5*HPL[{3}, x] - 720*HPL[{4}, x] + 1200*xi^2*HPL[{4}, x] - 480*xi^4*HPL[{4}, x] + 2400*xi*HPL[{-1, -1}, x] - 2880*xi^3*HPL[{-1, -1}, x] + 960*xi^5*HPL[{-1, -1}, x] - 120*Pi^2*HPL[{-1, 0}, x] + 200*Pi^2*xi^2*HPL[{-1, 0}, x] - 80*Pi^2*xi^4*HPL[{-1, 0}, x] + 2400*xi*HPL[{-1, 1}, x] - 2880*xi^3*HPL[{-1, 1}, x] + 960*xi^5*HPL[{-1, 1}, x] + 180*Pi^2*HPL[{0, 0}, x] + 600*xi*HPL[{0, 0}, x] - 300*Pi^2*xi^2*HPL[{0, 0}, x] - 240*xi^3*HPL[{0, 0}, x] + 120*Pi^2*xi^4*HPL[{0, 0}, x] - 270*xi^5*HPL[{0, 0}, x] + 30*xi^7*HPL[{0, 0}, x] + 2400*xi*HPL[{1, -1}, x] - 2880*xi^3*HPL[{1, -1}, x] + 960*xi^5*HPL[{1, -1}, x] - 120*Pi^2*HPL[{1, 0}, x] + 200*Pi^2*xi^2*HPL[{1, 0}, x] - 80*Pi^2*xi^4*HPL[{1, 0}, x] + 2400*xi*HPL[{1, 1}, x] - 2880*xi^3*HPL[{1, 1}, x] + 960*xi^5*HPL[{1, 1}, x] - 720*HPL[{-2, 0, 0}, x] + 1200*xi^2*HPL[{-2, 0, 0}, x] - 480*xi^4*HPL[{-2, 0, 0}, x] - 1440*xi*HPL[{-1, 0, 0}, x] + 1920*xi^3*HPL[{-1, 0, 0}, x] - 480*xi^5*HPL[{-1, 0, 0}, x] - 420*HPL[{0, 0, 0}, x] + 720*xi*HPL[{0, 0, 0}, x] + 900*xi^2*HPL[{0, 0, 0}, x] - 960*xi^3*HPL[{0, 0, 0}, x] - 540*xi^4*HPL[{0, 0, 0}, x] + 240*xi^5*HPL[{0, 0, 0}, x] + 60*xi^6*HPL[{0, 0, 0}, x] - 720*HPL[{-1, 0, 0, 0}, x] + 1200*xi^2*HPL[{-1, 0, 0, 0}, x] - 480*xi^4*HPL[{-1, 0, 0, 0}, x] + 360*HPL[{0, 0, 0, 0}, x] - 600*xi^2*HPL[{0, 0, 0, 0}, x] + 240*xi^4*HPL[{0, 0, 0, 0}, x] - 720*HPL[{1, 0, 0, 0}, x] + 1200*xi^2*HPL[{1, 0, 0, 0}, x] - 480*xi^4*HPL[{1, 0, 0, 0}, x] + 360*xi*Zeta[3] - 480*xi^3*Zeta[3] + 120*xi^5*Zeta[3] + 180*HPL[{0}, x]*Zeta[3] - 300*xi^2*HPL[{0}, x]*Zeta[3] + 120*xi^4*HPL[{0}, x]*Zeta[3]))/(15*xi^3*(-1 + xi^2))) + g^6*((8*(-108*Pi^4 - 9045*xi - 180*Pi^2*xi - 118*Pi^4*xi - 2160*Pi^2*xi^2 + 264*Pi^4*xi^2 + 6075*xi^3 - 180*Pi^2*xi^3 + 266*Pi^4*xi^3 + 3840*Pi^2*xi^4 - 204*Pi^4*xi^4 + 3780*xi^5 + 720*Pi^2*xi^5 - 178*Pi^4*xi^5 - 1920*Pi^2*xi^6 + 48*Pi^4*xi^6 - 1620*xi^7 - 360*Pi^2*xi^7 + 30*Pi^4*xi^7 + 240*Pi^2*xi^8 - 720*(-1 + xi^2)^2*(-9 + 4*xi^2)*HPL[{-4}, x] - 1440*xi*(-9 + 19*xi^2 - 12*xi^4 + 2*xi^6)*HPL[{-3}, x] + 1080*Pi^2*HPL[{-2}, x] + 12960*xi^2*HPL[{-2}, x] - 2640*Pi^2*xi^2*HPL[{-2}, x] - 23040*xi^4*HPL[{-2}, x] + 2040*Pi^2*xi^4*HPL[{-2}, x] + 11520*xi^6*HPL[{-2}, x] - 480*Pi^2*xi^6*HPL[{-2}, x] - 1440*xi^8*HPL[{-2}, x] + 13140*xi*HPL[{-1}, x] + 2160*Pi^2*xi*HPL[{-1}, x] - 15660*xi^3*HPL[{-1}, x] - 4560*Pi^2*xi^3*HPL[{-1}, x] + 2160*xi^5*HPL[{-1}, x] + 2880*Pi^2*xi^5*HPL[{-1}, x] + 720*xi^7*HPL[{-1}, x] - 480*Pi^2*xi^7*HPL[{-1}, x] + 120*Pi^2*HPL[{0}, x] - 80*Pi^4*HPL[{0}, x] - 2160*Pi^2*xi*HPL[{0}, x] - 14220*xi^2*HPL[{0}, x] - 1320*Pi^2*xi^2*HPL[{0}, x] + 204*Pi^4*xi^2*HPL[{0}, x] + 4560*Pi^2*xi^3*HPL[{0}, x] + 20880*xi^4*HPL[{0}, x] + 2280*Pi^2*xi^4*HPL[{0}, x] - 168*Pi^4*xi^4*HPL[{0}, x] - 2880*Pi^2*xi^5*HPL[{0}, x] - 7200*xi^6*HPL[{0}, x] - 1200*Pi^2*xi^6*HPL[{0}, x] + 44*Pi^4*xi^6*HPL[{0}, x] + 480*Pi^2*xi^7*HPL[{0}, x] + 180*xi^8*HPL[{0}, x] + 120*Pi^2*xi^8*HPL[{0}, x] + 13140*xi*HPL[{1}, x] + 2160*Pi^2*xi*HPL[{1}, x] - 15660*xi^3*HPL[{1}, x] - 4560*Pi^2*xi^3*HPL[{1}, x] + 2160*xi^5*HPL[{1}, x] + 2880*Pi^2*xi^5*HPL[{1}, x] + 720*xi^7*HPL[{1}, x] - 480*Pi^2*xi^7*HPL[{1}, x] + 1080*Pi^2*HPL[{2}, x] + 12960*xi^2*HPL[{2}, x] - 2640*Pi^2*xi^2*HPL[{2}, x] - 23040*xi^4*HPL[{2}, x] + 2040*Pi^2*xi^4*HPL[{2}, x] + 11520*xi^6*HPL[{2}, x] - 480*Pi^2*xi^6*HPL[{2}, x] - 1440*xi^8*HPL[{2}, x] + 12960*xi*HPL[{3}, x] - 27360*xi^3*HPL[{3}, x] + 17280*xi^5*HPL[{3}, x] - 2880*xi^7*HPL[{3}, x] + 6480*HPL[{4}, x] - 15840*xi^2*HPL[{4}, x] + 12240*xi^4*HPL[{4}, x] - 2880*xi^6*HPL[{4}, x] + 6480*HPL[{-3, 0}, x] - 15840*xi^2*HPL[{-3, 0}, x] + 12240*xi^4*HPL[{-3, 0}, x] - 2880*xi^6*HPL[{-3, 0}, x] + 12960*xi*HPL[{-2, 0}, x] - 27360*xi^3*HPL[{-2, 0}, x] + 17280*xi^5*HPL[{-2, 0}, x] - 2880*xi^7*HPL[{-2, 0}, x] - 14400*xi*HPL[{-1, -1}, x] + 25920*xi^3*HPL[{-1, -1}, x] - 14400*xi^5*HPL[{-1, -1}, x] + 2880*xi^7*HPL[{-1, -1}, x] + 1080*Pi^2*HPL[{-1, 0}, x] + 12960*xi^2*HPL[{-1, 0}, x] - 2640*Pi^2*xi^2*HPL[{-1, 0}, x] - 23040*xi^4*HPL[{-1, 0}, x] + 2040*Pi^2*xi^4*HPL[{-1, 0}, x] + 11520*xi^6*HPL[{-1, 0}, x] - 480*Pi^2*xi^6*HPL[{-1, 0}, x] - 1440*xi^8*HPL[{-1, 0}, x] - 14400*xi*HPL[{-1, 1}, x] + 25920*xi^3*HPL[{-1, 1}, x] - 14400*xi^5*HPL[{-1, 1}, x] + 2880*xi^7*HPL[{-1, 1}, x] - 1080*Pi^2*HPL[{0, 0}, x] - 6390*xi*HPL[{0, 0}, x] - 1320*Pi^2*xi*HPL[{0, 0}, x] - 6480*xi^2*HPL[{0, 0}, x] + 2640*Pi^2*xi^2*HPL[{0, 0}, x] + 6570*xi^3*HPL[{0, 0}, x] + 3000*Pi^2*xi^3*HPL[{0, 0}, x] + 11520*xi^4*HPL[{0, 0}, x] - 2040*Pi^2*xi^4*HPL[{0, 0}, x] + 2880*xi^5*HPL[{0, 0}, x] - 2040*Pi^2*xi^5*HPL[{0, 0}, x] - 5760*xi^6*HPL[{0, 0}, x] + 480*Pi^2*xi^6*HPL[{0, 0}, x] - 3330*xi^7*HPL[{0, 0}, x] + 360*Pi^2*xi^7*HPL[{0, 0}, x] + 720*xi^8*HPL[{0, 0}, x] + 270*xi^9*HPL[{0, 0}, x] - 14400*xi*HPL[{1, -1}, x] + 25920*xi^3*HPL[{1, -1}, x] - 14400*xi^5*HPL[{1, -1}, x] + 2880*xi^7*HPL[{1, -1}, x] + 1080*Pi^2*HPL[{1, 0}, x] - 2640*Pi^2*xi^2*HPL[{1, 0}, x] + 2040*Pi^2*xi^4*HPL[{1, 0}, x] - 480*Pi^2*xi^6*HPL[{1, 0}, x] - 14400*xi*HPL[{1, 1}, x] + 25920*xi^3*HPL[{1, 1}, x] - 14400*xi^5*HPL[{1, 1}, x] + 2880*xi^7*HPL[{1, 1}, x] + 6480*HPL[{-2, 0, 0}, x] - 15840*xi^2*HPL[{-2, 0, 0}, x] + 12240*xi^4*HPL[{-2, 0, 0}, x] - 2880*xi^6*HPL[{-2, 0, 0}, x] + 12960*xi*HPL[{-1, 0, 0}, x] - 27360*xi^3*HPL[{-1, 0, 0}, x] + 17280*xi^5*HPL[{-1, 0, 0}, x] - 2880*xi^7*HPL[{-1, 0, 0}, x] + 720*HPL[{0, 0, 0}, x] - 840*Pi^2*HPL[{0, 0, 0}, x] - 9720*xi*HPL[{0, 0, 0}, x] - 12240*xi^2*HPL[{0, 0, 0}, x] + 2160*Pi^2*xi^2*HPL[{0, 0, 0}, x] + 20520*xi^3*HPL[{0, 0, 0}, x] + 22320*xi^4*HPL[{0, 0, 0}, x] - 1800*Pi^2*xi^4*HPL[{0, 0, 0}, x] - 12960*xi^5*HPL[{0, 0, 0}, x] - 12240*xi^6*HPL[{0, 0, 0}, x] + 480*Pi^2*xi^6*HPL[{0, 0, 0}, x] + 2160*xi^7*HPL[{0, 0, 0}, x] + 1440*xi^8*HPL[{0, 0, 0}, x] + 6480*xi*HPL[{1, 0, 0}, x] - 13680*xi^3*HPL[{1, 0, 0}, x] + 8640*xi^5*HPL[{1, 0, 0}, x] - 1440*xi^7*HPL[{1, 0, 0}, x] + 3240*HPL[{2, 0, 0}, x] - 7920*xi^2*HPL[{2, 0, 0}, x] + 6120*xi^4*HPL[{2, 0, 0}, x] - 1440*xi^6*HPL[{2, 0, 0}, x] + 6480*HPL[{-1, 0, 0, 0}, x] - 15840*xi^2*HPL[{-1, 0, 0, 0}, x] + 12240*xi^4*HPL[{-1, 0, 0, 0}, x] - 2880*xi^6*HPL[{-1, 0, 0, 0}, x] - 4860*HPL[{0, 0, 0, 0}, x] - 12240*xi*HPL[{0, 0, 0, 0}, x] + 11880*xi^2*HPL[{0, 0, 0, 0}, x] + 28080*xi^3*HPL[{0, 0, 0, 0}, x] - 9180*xi^4*HPL[{0, 0, 0, 0}, x] - 19440*xi^5*HPL[{0, 0, 0, 0}, x] + 2160*xi^6*HPL[{0, 0, 0, 0}, x] + 3600*xi^7*HPL[{0, 0, 0, 0}, x] + 6480*HPL[{1, 0, 0, 0}, x] - 15840*xi^2*HPL[{1, 0, 0, 0}, x] + 12240*xi^4*HPL[{1, 0, 0, 0}, x] - 2880*xi^6*HPL[{1, 0, 0, 0}, x] - 7200*HPL[{0, 0, 0, 0, 0}, x] + 18720*xi^2*HPL[{0, 0, 0, 0, 0}, x] - 15840*xi^4*HPL[{0, 0, 0, 0, 0}, x] + 4320*xi^6*HPL[{0, 0, 0, 0, 0}, x])*Log[Y])/(45*xi^3*(-1 + xi^2)^2) - (8*(-219*xi - 36*Pi^2*xi + 261*xi^3 + 76*Pi^2*xi^3 - 36*xi^5 - 48*Pi^2*xi^5 - 12*xi^7 + 8*Pi^2*xi^7 - 48*xi*(-5 + 9*xi^2 - 5*xi^4 + xi^6)*HPL[{-1}, x] + 2*(-1 + xi^2)*(12*xi^2*(9 - 7*xi^2 + xi^4) + Pi^2*(9 - 13*xi^2 + 4*xi^4))*HPL[{0}, x] + 240*xi*HPL[{1}, x] - 432*xi^3*HPL[{1}, x] + 240*xi^5*HPL[{1}, x] - 48*xi^7*HPL[{1}, x] - 216*xi*HPL[{0, 0}, x] + 456*xi^3*HPL[{0, 0}, x] - 288*xi^5*HPL[{0, 0}, x] + 48*xi^7*HPL[{0, 0}, x] - 108*HPL[{0, 0, 0}, x] + 264*xi^2*HPL[{0, 0, 0}, x] - 204*xi^4*HPL[{0, 0, 0}, x] + 48*xi^6*HPL[{0, 0, 0}, x])*Log[Y]^2)/(3*xi^3*(-1 + xi^2)^2) + (64*(5 - 4*xi^2 + xi^4)*Log[Y]^3)/(3*xi^2*(-1 + xi^2)) - (4*(630*Pi^4 - 1188*Pi^6 - 487620*xi + 35280*Pi^2*xi - 6552*Pi^4*xi - 177660*Pi^2*xi^2 - 17976*Pi^4*xi^2 + 2956*Pi^6*xi^2 + 170100*xi^3 - 88200*Pi^2*xi^3 + 11592*Pi^4*xi^3 + 246960*Pi^2*xi^4 + 34062*Pi^4*xi^4 - 2348*Pi^6*xi^4 + 306180*xi^5 + 70560*Pi^2*xi^5 - 4536*Pi^4*xi^5 - 70560*Pi^2*xi^6 - 18648*Pi^4*xi^6 + 580*Pi^6*xi^6 - 79380*xi^7 - 17640*Pi^2*xi^7 - 504*Pi^4*xi^7 - 3780*Pi^2*xi^8 + 1932*Pi^4*xi^8 - 120960*(-1 + xi^2)^2*(-5 + 3*xi^2)*HPL[{-6}, x] - 15120*(-1 + xi^2)^2*(-27 - 68*xi + 12*xi^2 + 20*xi^3)*HPL[{-5}, x] - 60480*HPL[{-4}, x] + 70560*Pi^2*HPL[{-4}, x] + 816480*xi*HPL[{-4}, x] + 1028160*xi^2*HPL[{-4}, x] - 181440*Pi^2*xi^2*HPL[{-4}, x] - 1723680*xi^3*HPL[{-4}, x] - 1874880*xi^4*HPL[{-4}, x] + 151200*Pi^2*xi^4*HPL[{-4}, x] + 1088640*xi^5*HPL[{-4}, x] + 1028160*xi^6*HPL[{-4}, x] - 40320*Pi^2*xi^6*HPL[{-4}, x] - 181440*xi^7*HPL[{-4}, x] - 120960*xi^8*HPL[{-4}, x] + 136080*Pi^2*HPL[{-3}, x] + 536760*xi*HPL[{-3}, x] + 110880*Pi^2*xi*HPL[{-3}, x] + 544320*xi^2*HPL[{-3}, x] - 332640*Pi^2*xi^2*HPL[{-3}, x] - 551880*xi^3*HPL[{-3}, x] - 252000*Pi^2*xi^3*HPL[{-3}, x] - 967680*xi^4*HPL[{-3}, x] + 257040*Pi^2*xi^4*HPL[{-3}, x] - 241920*xi^5*HPL[{-3}, x] + 171360*Pi^2*xi^5*HPL[{-3}, x] + 483840*xi^6*HPL[{-3}, x] - 60480*Pi^2*xi^6*HPL[{-3}, x] + 279720*xi^7*HPL[{-3}, x] - 30240*Pi^2*xi^7*HPL[{-3}, x] - 60480*xi^8*HPL[{-3}, x] - 22680*xi^9*HPL[{-3}, x] - 10080*Pi^2*HPL[{-2}, x] + 6720*Pi^4*HPL[{-2}, x] + 272160*Pi^2*xi*HPL[{-2}, x] + 1194480*xi^2*HPL[{-2}, x] + 110880*Pi^2*xi^2*HPL[{-2}, x] - 17136*Pi^4*xi^2*HPL[{-2}, x] - 574560*Pi^2*xi^3*HPL[{-2}, x] - 1753920*xi^4*HPL[{-2}, x] - 191520*Pi^2*xi^4*HPL[{-2}, x] + 14112*Pi^4*xi^4*HPL[{-2}, x] + 362880*Pi^2*xi^5*HPL[{-2}, x] + 604800*xi^6*HPL[{-2}, x] + 100800*Pi^2*xi^6*HPL[{-2}, x] - 3696*Pi^4*xi^6*HPL[{-2}, x] - 60480*Pi^2*xi^7*HPL[{-2}, x] - 15120*xi^8*HPL[{-2}, x] - 10080*Pi^2*xi^8*HPL[{-2}, x] + 9072*Pi^4*HPL[{-1}, x] + 759780*xi*HPL[{-1}, x] + 15120*Pi^2*xi*HPL[{-1}, x] + 9912*Pi^4*xi*HPL[{-1}, x] + 272160*Pi^2*xi^2*HPL[{-1}, x] - 22176*Pi^4*xi^2*HPL[{-1}, x] - 510300*xi^3*HPL[{-1}, x] + 15120*Pi^2*xi^3*HPL[{-1}, x] - 22344*Pi^4*xi^3*HPL[{-1}, x] - 483840*Pi^2*xi^4*HPL[{-1}, x] + 17136*Pi^4*xi^4*HPL[{-1}, x] - 317520*xi^5*HPL[{-1}, x] - 60480*Pi^2*xi^5*HPL[{-1}, x] + 14952*Pi^4*xi^5*HPL[{-1}, x] + 241920*Pi^2*xi^6*HPL[{-1}, x] - 4032*Pi^4*xi^6*HPL[{-1}, x] + 136080*xi^7*HPL[{-1}, x] + 30240*Pi^2*xi^7*HPL[{-1}, x] - 2520*Pi^4*xi^7*HPL[{-1}, x] - 30240*Pi^2*xi^8*HPL[{-1}, x] + 10710*Pi^2*HPL[{0}, x] - 1743*Pi^4*HPL[{0}, x] - 58590*Pi^2*xi*HPL[{0}, x] - 23772*Pi^4*xi*HPL[{0}, x] - 895860*xi^2*HPL[{0}, x] - 177660*Pi^2*xi^2*HPL[{0}, x] + 2394*Pi^4*xi^2*HPL[{0}, x] + 42210*Pi^2*xi^3*HPL[{0}, x] + 53844*Pi^4*xi^3*HPL[{0}, x] + 1028160*xi^4*HPL[{0}, x] + 277830*Pi^2*xi^4*HPL[{0}, x] + 756*Pi^4*xi^4*HPL[{0}, x] + 60480*Pi^2*xi^5*HPL[{0}, x] - 36372*Pi^4*xi^5*HPL[{0}, x] - 151200*xi^6*HPL[{0}, x] - 118440*Pi^2*xi^6*HPL[{0}, x] - 1722*Pi^4*xi^6*HPL[{0}, x] - 47250*Pi^2*xi^7*HPL[{0}, x] + 6300*Pi^4*xi^7*HPL[{0}, x] - 49140*xi^8*HPL[{0}, x] + 7560*Pi^2*xi^8*HPL[{0}, x] + 315*Pi^4*xi^8*HPL[{0}, x] + 3150*Pi^2*xi^9*HPL[{0}, x] + 9072*Pi^4*HPL[{1}, x] + 759780*xi*HPL[{1}, x] + 15120*Pi^2*xi*HPL[{1}, x] + 9912*Pi^4*xi*HPL[{1}, x] - 22176*Pi^4*xi^2*HPL[{1}, x] - 510300*xi^3*HPL[{1}, x] + 15120*Pi^2*xi^3*HPL[{1}, x] - 22344*Pi^4*xi^3*HPL[{1}, x] + 17136*Pi^4*xi^4*HPL[{1}, x] - 317520*xi^5*HPL[{1}, x] - 60480*Pi^2*xi^5*HPL[{1}, x] + 14952*Pi^4*xi^5*HPL[{1}, x] - 4032*Pi^4*xi^6*HPL[{1}, x] + 136080*xi^7*HPL[{1}, x] + 30240*Pi^2*xi^7*HPL[{1}, x] - 2520*Pi^4*xi^7*HPL[{1}, x] - 10080*Pi^2*HPL[{2}, x] + 6720*Pi^4*HPL[{2}, x] + 1194480*xi^2*HPL[{2}, x] + 110880*Pi^2*xi^2*HPL[{2}, x] - 17136*Pi^4*xi^2*HPL[{2}, x] - 1753920*xi^4*HPL[{2}, x] - 191520*Pi^2*xi^4*HPL[{2}, x] + 14112*Pi^4*xi^4*HPL[{2}, x] + 604800*xi^6*HPL[{2}, x] + 100800*Pi^2*xi^6*HPL[{2}, x] - 3696*Pi^4*xi^6*HPL[{2}, x] - 15120*xi^8*HPL[{2}, x] - 10080*Pi^2*xi^8*HPL[{2}, x] + 536760*xi*HPL[{3}, x] + 110880*Pi^2*xi*HPL[{3}, x] + 544320*xi^2*HPL[{3}, x] - 551880*xi^3*HPL[{3}, x] - 252000*Pi^2*xi^3*HPL[{3}, x] - 967680*xi^4*HPL[{3}, x] - 241920*xi^5*HPL[{3}, x] + 171360*Pi^2*xi^5*HPL[{3}, x] + 483840*xi^6*HPL[{3}, x] + 279720*xi^7*HPL[{3}, x] - 30240*Pi^2*xi^7*HPL[{3}, x] - 60480*xi^8*HPL[{3}, x] - 22680*xi^9*HPL[{3}, x] - 60480*HPL[{4}, x] + 70560*Pi^2*HPL[{4}, x] + 816480*xi*HPL[{4}, x] + 1028160*xi^2*HPL[{4}, x] - 181440*Pi^2*xi^2*HPL[{4}, x] - 1723680*xi^3*HPL[{4}, x] - 1874880*xi^4*HPL[{4}, x] + 151200*Pi^2*xi^4*HPL[{4}, x] + 1088640*xi^5*HPL[{4}, x] + 1028160*xi^6*HPL[{4}, x] - 40320*Pi^2*xi^6*HPL[{4}, x] - 181440*xi^7*HPL[{4}, x] - 120960*xi^8*HPL[{4}, x] + 408240*HPL[{5}, x] + 1028160*xi*HPL[{5}, x] - 997920*xi^2*HPL[{5}, x] - 2358720*xi^3*HPL[{5}, x] + 771120*xi^4*HPL[{5}, x] + 1632960*xi^5*HPL[{5}, x] - 181440*xi^6*HPL[{5}, x] - 302400*xi^7*HPL[{5}, x] + 604800*HPL[{6}, x] - 1572480*xi^2*HPL[{6}, x] + 1330560*xi^4*HPL[{6}, x] - 362880*xi^6*HPL[{6}, x] + 362880*HPL[{-5, 0}, x] - 967680*xi^2*HPL[{-5, 0}, x] + 846720*xi^4*HPL[{-5, 0}, x] - 241920*xi^6*HPL[{-5, 0}, x] - 544320*HPL[{-4, -1}, x] + 1330560*xi^2*HPL[{-4, -1}, x] - 1028160*xi^4*HPL[{-4, -1}, x] + 241920*xi^6*HPL[{-4, -1}, x] + 272160*HPL[{-4, 0}, x] + 725760*xi*HPL[{-4, 0}, x] - 665280*xi^2*HPL[{-4, 0}, x] - 1693440*xi^3*HPL[{-4, 0}, x] + 514080*xi^4*HPL[{-4, 0}, x] + 1209600*xi^5*HPL[{-4, 0}, x] - 120960*xi^6*HPL[{-4, 0}, x] - 241920*xi^7*HPL[{-4, 0}, x] - 544320*HPL[{-4, 1}, x] + 1330560*xi^2*HPL[{-4, 1}, x] - 1028160*xi^4*HPL[{-4, 1}, x] + 241920*xi^6*HPL[{-4, 1}, x] - 544320*HPL[{-3, -2}, x] + 1330560*xi^2*HPL[{-3, -2}, x] - 1028160*xi^4*HPL[{-3, -2}, x] + 241920*xi^6*HPL[{-3, -2}, x] - 1088640*xi*HPL[{-3, -1}, x] + 2298240*xi^3*HPL[{-3, -1}, x] - 1451520*xi^5*HPL[{-3, -1}, x] + 241920*xi^7*HPL[{-3, -1}, x] - 90720*HPL[{-3, 0}, x] + 70560*Pi^2*HPL[{-3, 0}, x] + 544320*xi*HPL[{-3, 0}, x] + 1028160*xi^2*HPL[{-3, 0}, x] - 181440*Pi^2*xi^2*HPL[{-3, 0}, x] - 1149120*xi^3*HPL[{-3, 0}, x] - 1784160*xi^4*HPL[{-3, 0}, x] + 151200*Pi^2*xi^4*HPL[{-3, 0}, x] + 725760*xi^5*HPL[{-3, 0}, x] + 967680*xi^6*HPL[{-3, 0}, x] - 40320*Pi^2*xi^6*HPL[{-3, 0}, x] - 120960*xi^7*HPL[{-3, 0}, x] - 120960*xi^8*HPL[{-3, 0}, x] - 1088640*xi*HPL[{-3, 1}, x] + 2298240*xi^3*HPL[{-3, 1}, x] - 1451520*xi^5*HPL[{-3, 1}, x] + 241920*xi^7*HPL[{-3, 1}, x] - 544320*HPL[{-3, 2}, x] + 1330560*xi^2*HPL[{-3, 2}, x] - 1028160*xi^4*HPL[{-3, 2}, x] + 241920*xi^6*HPL[{-3, 2}, x] - 544320*HPL[{-2, -3}, x] + 1330560*xi^2*HPL[{-2, -3}, x] - 1028160*xi^4*HPL[{-2, -3}, x] + 241920*xi^6*HPL[{-2, -3}, x] - 1088640*xi*HPL[{-2, -2}, x] + 2298240*xi^3*HPL[{-2, -2}, x] - 1451520*xi^5*HPL[{-2, -2}, x] + 241920*xi^7*HPL[{-2, -2}, x] - 90720*Pi^2*HPL[{-2, -1}, x] - 1088640*xi^2*HPL[{-2, -1}, x] + 221760*Pi^2*xi^2*HPL[{-2, -1}, x] + 1935360*xi^4*HPL[{-2, -1}, x] - 171360*Pi^2*xi^4*HPL[{-2, -1}, x] - 967680*xi^6*HPL[{-2, -1}, x] + 40320*Pi^2*xi^6*HPL[{-2, -1}, x] + 120960*xi^8*HPL[{-2, -1}, x] + 90720*Pi^2*HPL[{-2, 0}, x] + 907200*xi*HPL[{-2, 0}, x] + 110880*Pi^2*xi*HPL[{-2, 0}, x] - 221760*Pi^2*xi^2*HPL[{-2, 0}, x] - 1149120*xi^3*HPL[{-2, 0}, x] - 252000*Pi^2*xi^3*HPL[{-2, 0}, x] + 171360*Pi^2*xi^4*HPL[{-2, 0}, x] + 171360*Pi^2*xi^5*HPL[{-2, 0}, x] - 40320*Pi^2*xi^6*HPL[{-2, 0}, x] + 272160*xi^7*HPL[{-2, 0}, x] - 30240*Pi^2*xi^7*HPL[{-2, 0}, x] - 30240*xi^9*HPL[{-2, 0}, x] - 90720*Pi^2*HPL[{-2, 1}, x] - 1088640*xi^2*HPL[{-2, 1}, x] + 221760*Pi^2*xi^2*HPL[{-2, 1}, x] + 1935360*xi^4*HPL[{-2, 1}, x] - 171360*Pi^2*xi^4*HPL[{-2, 1}, x] - 967680*xi^6*HPL[{-2, 1}, x] + 40320*Pi^2*xi^6*HPL[{-2, 1}, x] + 120960*xi^8*HPL[{-2, 1}, x] - 1088640*xi*HPL[{-2, 2}, x] + 2298240*xi^3*HPL[{-2, 2}, x] - 1451520*xi^5*HPL[{-2, 2}, x] + 241920*xi^7*HPL[{-2, 2}, x] - 544320*HPL[{-2, 3}, x] + 1330560*xi^2*HPL[{-2, 3}, x] - 1028160*xi^4*HPL[{-2, 3}, x] + 241920*xi^6*HPL[{-2, 3}, x] - 544320*HPL[{-1, -4}, x] + 1330560*xi^2*HPL[{-1, -4}, x] - 1028160*xi^4*HPL[{-1, -4}, x] + 241920*xi^6*HPL[{-1, -4}, x] - 1088640*xi*HPL[{-1, -3}, x] + 2298240*xi^3*HPL[{-1, -3}, x] - 1451520*xi^5*HPL[{-1, -3}, x] + 241920*xi^7*HPL[{-1, -3}, x] - 90720*Pi^2*HPL[{-1, -2}, x] - 1088640*xi^2*HPL[{-1, -2}, x] + 221760*Pi^2*xi^2*HPL[{-1, -2}, x] + 1935360*xi^4*HPL[{-1, -2}, x] - 171360*Pi^2*xi^4*HPL[{-1, -2}, x] - 967680*xi^6*HPL[{-1, -2}, x] + 40320*Pi^2*xi^6*HPL[{-1, -2}, x] + 120960*xi^8*HPL[{-1, -2}, x] - 1103760*xi*HPL[{-1, -1}, x] - 181440*Pi^2*xi*HPL[{-1, -1}, x] + 1315440*xi^3*HPL[{-1, -1}, x] + 383040*Pi^2*xi^3*HPL[{-1, -1}, x] - 181440*xi^5*HPL[{-1, -1}, x] - 241920*Pi^2*xi^5*HPL[{-1, -1}, x] - 60480*xi^7*HPL[{-1, -1}, x] + 40320*Pi^2*xi^7*HPL[{-1, -1}, x] - 10080*Pi^2*HPL[{-1, 0}, x] + 6720*Pi^4*HPL[{-1, 0}, x] + 181440*Pi^2*xi*HPL[{-1, 0}, x] + 1451520*xi^2*HPL[{-1, 0}, x] + 110880*Pi^2*xi^2*HPL[{-1, 0}, x] - 17136*Pi^4*xi^2*HPL[{-1, 0}, x] - 383040*Pi^2*xi^3*HPL[{-1, 0}, x] - 2298240*xi^4*HPL[{-1, 0}, x] - 191520*Pi^2*xi^4*HPL[{-1, 0}, x] + 14112*Pi^4*xi^4*HPL[{-1, 0}, x] + 241920*Pi^2*xi^5*HPL[{-1, 0}, x] + 967680*xi^6*HPL[{-1, 0}, x] + 100800*Pi^2*xi^6*HPL[{-1, 0}, x] - 3696*Pi^4*xi^6*HPL[{-1, 0}, x] - 40320*Pi^2*xi^7*HPL[{-1, 0}, x] - 90720*xi^8*HPL[{-1, 0}, x] - 10080*Pi^2*xi^8*HPL[{-1, 0}, x] - 1103760*xi*HPL[{-1, 1}, x] - 181440*Pi^2*xi*HPL[{-1, 1}, x] + 1315440*xi^3*HPL[{-1, 1}, x] + 383040*Pi^2*xi^3*HPL[{-1, 1}, x] - 181440*xi^5*HPL[{-1, 1}, x] - 241920*Pi^2*xi^5*HPL[{-1, 1}, x] - 60480*xi^7*HPL[{-1, 1}, x] + 40320*Pi^2*xi^7*HPL[{-1, 1}, x] - 90720*Pi^2*HPL[{-1, 2}, x] - 1088640*xi^2*HPL[{-1, 2}, x] + 221760*Pi^2*xi^2*HPL[{-1, 2}, x] + 1935360*xi^4*HPL[{-1, 2}, x] - 171360*Pi^2*xi^4*HPL[{-1, 2}, x] - 967680*xi^6*HPL[{-1, 2}, x] + 40320*Pi^2*xi^6*HPL[{-1, 2}, x] + 120960*xi^8*HPL[{-1, 2}, x] - 1088640*xi*HPL[{-1, 3}, x] + 2298240*xi^3*HPL[{-1, 3}, x] - 1451520*xi^5*HPL[{-1, 3}, x] + 241920*xi^7*HPL[{-1, 3}, x] - 544320*HPL[{-1, 4}, x] + 1330560*xi^2*HPL[{-1, 4}, x] - 1028160*xi^4*HPL[{-1, 4}, x] + 241920*xi^6*HPL[{-1, 4}, x] + 7560*Pi^2*HPL[{0, 0}, x] - 15540*Pi^4*HPL[{0, 0}, x] - 149310*xi*HPL[{0, 0}, x] - 151200*Pi^2*xi*HPL[{0, 0}, x] - 725760*xi^2*HPL[{0, 0}, x] - 191520*Pi^2*xi^2*HPL[{0, 0}, x] + 39816*Pi^4*xi^2*HPL[{0, 0}, x] - 300510*xi^3*HPL[{0, 0}, x] + 292320*Pi^2*xi^3*HPL[{0, 0}, x] + 1149120*xi^4*HPL[{0, 0}, x] + 360360*Pi^2*xi^4*HPL[{0, 0}, x] - 33012*Pi^4*xi^4*HPL[{0, 0}, x] + 695520*xi^5*HPL[{0, 0}, x] - 149940*Pi^2*xi^5*HPL[{0, 0}, x] - 483840*xi^6*HPL[{0, 0}, x] - 199080*Pi^2*xi^6*HPL[{0, 0}, x] + 8736*Pi^4*xi^6*HPL[{0, 0}, x] - 266490*xi^7*HPL[{0, 0}, x] + 7560*Pi^2*xi^7*HPL[{0, 0}, x] + 45360*xi^8*HPL[{0, 0}, x] + 22680*Pi^2*xi^8*HPL[{0, 0}, x] + 5670*xi^9*HPL[{0, 0}, x] + 1260*Pi^2*xi^9*HPL[{0, 0}, x] - 544320*HPL[{1, -4}, x] + 1330560*xi^2*HPL[{1, -4}, x] - 1028160*xi^4*HPL[{1, -4}, x] + 241920*xi^6*HPL[{1, -4}, x] - 544320*xi*HPL[{1, -3}, x] + 1149120*xi^3*HPL[{1, -3}, x] - 725760*xi^5*HPL[{1, -3}, x] + 120960*xi^7*HPL[{1, -3}, x] - 90720*Pi^2*HPL[{1, -2}, x] + 221760*Pi^2*xi^2*HPL[{1, -2}, x] - 171360*Pi^2*xi^4*HPL[{1, -2}, x] + 40320*Pi^2*xi^6*HPL[{1, -2}, x] - 1103760*xi*HPL[{1, -1}, x] - 181440*Pi^2*xi*HPL[{1, -1}, x] + 1315440*xi^3*HPL[{1, -1}, x] + 383040*Pi^2*xi^3*HPL[{1, -1}, x] - 181440*xi^5*HPL[{1, -1}, x] - 241920*Pi^2*xi^5*HPL[{1, -1}, x] - 60480*xi^7*HPL[{1, -1}, x] + 40320*Pi^2*xi^7*HPL[{1, -1}, x] - 10080*Pi^2*HPL[{1, 0}, x] + 6720*Pi^4*HPL[{1, 0}, x] + 136080*Pi^2*xi*HPL[{1, 0}, x] + 70560*Pi^2*xi^2*HPL[{1, 0}, x] - 17136*Pi^4*xi^2*HPL[{1, 0}, x] - 287280*Pi^2*xi^3*HPL[{1, 0}, x] - 110880*Pi^2*xi^4*HPL[{1, 0}, x] + 14112*Pi^4*xi^4*HPL[{1, 0}, x] + 181440*Pi^2*xi^5*HPL[{1, 0}, x] + 55440*Pi^2*xi^6*HPL[{1, 0}, x] - 3696*Pi^4*xi^6*HPL[{1, 0}, x] - 30240*Pi^2*xi^7*HPL[{1, 0}, x] - 5040*Pi^2*xi^8*HPL[{1, 0}, x] - 1103760*xi*HPL[{1, 1}, x] - 181440*Pi^2*xi*HPL[{1, 1}, x] + 1315440*xi^3*HPL[{1, 1}, x] + 383040*Pi^2*xi^3*HPL[{1, 1}, x] - 181440*xi^5*HPL[{1, 1}, x] - 241920*Pi^2*xi^5*HPL[{1, 1}, x] - 60480*xi^7*HPL[{1, 1}, x] + 40320*Pi^2*xi^7*HPL[{1, 1}, x] - 90720*Pi^2*HPL[{1, 2}, x] + 221760*Pi^2*xi^2*HPL[{1, 2}, x] - 171360*Pi^2*xi^4*HPL[{1, 2}, x] + 40320*Pi^2*xi^6*HPL[{1, 2}, x] - 544320*xi*HPL[{1, 3}, x] + 1149120*xi^3*HPL[{1, 3}, x] - 725760*xi^5*HPL[{1, 3}, x] + 120960*xi^7*HPL[{1, 3}, x] - 544320*HPL[{1, 4}, x] + 1330560*xi^2*HPL[{1, 4}, x] - 1028160*xi^4*HPL[{1, 4}, x] + 241920*xi^6*HPL[{1, 4}, x] - 272160*HPL[{2, -3}, x] + 665280*xi^2*HPL[{2, -3}, x] - 514080*xi^4*HPL[{2, -3}, x] + 120960*xi^6*HPL[{2, -3}, x] - 90720*Pi^2*HPL[{2, -1}, x] - 1088640*xi^2*HPL[{2, -1}, x] + 221760*Pi^2*xi^2*HPL[{2, -1}, x] + 1935360*xi^4*HPL[{2, -1}, x] - 171360*Pi^2*xi^4*HPL[{2, -1}, x] - 967680*xi^6*HPL[{2, -1}, x] + 40320*Pi^2*xi^6*HPL[{2, -1}, x] + 120960*xi^8*HPL[{2, -1}, x] + 68040*Pi^2*HPL[{2, 0}, x] + 55440*Pi^2*xi*HPL[{2, 0}, x] - 166320*Pi^2*xi^2*HPL[{2, 0}, x] - 126000*Pi^2*xi^3*HPL[{2, 0}, x] + 128520*Pi^2*xi^4*HPL[{2, 0}, x] + 85680*Pi^2*xi^5*HPL[{2, 0}, x] - 30240*Pi^2*xi^6*HPL[{2, 0}, x] - 15120*Pi^2*xi^7*HPL[{2, 0}, x] - 90720*Pi^2*HPL[{2, 1}, x] - 1088640*xi^2*HPL[{2, 1}, x] + 221760*Pi^2*xi^2*HPL[{2, 1}, x] + 1935360*xi^4*HPL[{2, 1}, x] - 171360*Pi^2*xi^4*HPL[{2, 1}, x] - 967680*xi^6*HPL[{2, 1}, x] + 40320*Pi^2*xi^6*HPL[{2, 1}, x] + 120960*xi^8*HPL[{2, 1}, x] - 272160*HPL[{2, 3}, x] + 665280*xi^2*HPL[{2, 3}, x] - 514080*xi^4*HPL[{2, 3}, x] + 120960*xi^6*HPL[{2, 3}, x] - 1088640*xi*HPL[{3, -1}, x] + 2298240*xi^3*HPL[{3, -1}, x] - 1451520*xi^5*HPL[{3, -1}, x] + 241920*xi^7*HPL[{3, -1}, x] + 35280*Pi^2*HPL[{3, 0}, x] - 90720*Pi^2*xi^2*HPL[{3, 0}, x] + 75600*Pi^2*xi^4*HPL[{3, 0}, x] - 20160*Pi^2*xi^6*HPL[{3, 0}, x] - 1088640*xi*HPL[{3, 1}, x] + 2298240*xi^3*HPL[{3, 1}, x] - 1451520*xi^5*HPL[{3, 1}, x] + 241920*xi^7*HPL[{3, 1}, x] - 544320*HPL[{4, -1}, x] + 1330560*xi^2*HPL[{4, -1}, x] - 1028160*xi^4*HPL[{4, -1}, x] + 241920*xi^6*HPL[{4, -1}, x] - 544320*HPL[{4, 1}, x] + 1330560*xi^2*HPL[{4, 1}, x] - 1028160*xi^4*HPL[{4, 1}, x] + 241920*xi^6*HPL[{4, 1}, x] + 604800*HPL[{-4, 0, 0}, x] - 1572480*xi^2*HPL[{-4, 0, 0}, x] + 1330560*xi^4*HPL[{-4, 0, 0}, x] - 362880*xi^6*HPL[{-4, 0, 0}, x] + 136080*HPL[{-3, 0, 0}, x] + 1028160*xi*HPL[{-3, 0, 0}, x] - 332640*xi^2*HPL[{-3, 0, 0}, x] - 2358720*xi^3*HPL[{-3, 0, 0}, x] + 257040*xi^4*HPL[{-3, 0, 0}, x] + 1632960*xi^5*HPL[{-3, 0, 0}, x] - 60480*xi^6*HPL[{-3, 0, 0}, x] - 302400*xi^7*HPL[{-3, 0, 0}, x] - 544320*HPL[{-2, -2, 0}, x] + 1330560*xi^2*HPL[{-2, -2, 0}, x] - 1028160*xi^4*HPL[{-2, -2, 0}, x] + 241920*xi^6*HPL[{-2, -2, 0}, x] - 60480*HPL[{-2, 0, 0}, x] + 70560*Pi^2*HPL[{-2, 0, 0}, x] + 272160*xi*HPL[{-2, 0, 0}, x] + 1028160*xi^2*HPL[{-2, 0, 0}, x] - 181440*Pi^2*xi^2*HPL[{-2, 0, 0}, x] - 574560*xi^3*HPL[{-2, 0, 0}, x] - 1874880*xi^4*HPL[{-2, 0, 0}, x] + 151200*Pi^2*xi^4*HPL[{-2, 0, 0}, x] + 362880*xi^5*HPL[{-2, 0, 0}, x] + 1028160*xi^6*HPL[{-2, 0, 0}, x] - 40320*Pi^2*xi^6*HPL[{-2, 0, 0}, x] - 60480*xi^7*HPL[{-2, 0, 0}, x] - 120960*xi^8*HPL[{-2, 0, 0}, x] - 544320*HPL[{-1, -3, 0}, x] + 1330560*xi^2*HPL[{-1, -3, 0}, x] - 1028160*xi^4*HPL[{-1, -3, 0}, x] + 241920*xi^6*HPL[{-1, -3, 0}, x] - 1088640*xi*HPL[{-1, -2, 0}, x] + 2298240*xi^3*HPL[{-1, -2, 0}, x] - 1451520*xi^5*HPL[{-1, -2, 0}, x] + 241920*xi^7*HPL[{-1, -2, 0}, x] + 1209600*xi*HPL[{-1, -1, -1}, x] - 2177280*xi^3*HPL[{-1, -1, -1}, x] + 1209600*xi^5*HPL[{-1, -1, -1}, x] - 241920*xi^7*HPL[{-1, -1, -1}, x] - 90720*Pi^2*HPL[{-1, -1, 0}, x] + 221760*Pi^2*xi^2*HPL[{-1, -1, 0}, x] - 171360*Pi^2*xi^4*HPL[{-1, -1, 0}, x] + 40320*Pi^2*xi^6*HPL[{-1, -1, 0}, x] + 1209600*xi*HPL[{-1, -1, 1}, x] - 2177280*xi^3*HPL[{-1, -1, 1}, x] + 1209600*xi^5*HPL[{-1, -1, 1}, x] - 241920*xi^7*HPL[{-1, -1, 1}, x] + 90720*Pi^2*HPL[{-1, 0, 0}, x] + 536760*xi*HPL[{-1, 0, 0}, x] + 110880*Pi^2*xi*HPL[{-1, 0, 0}, x] - 221760*Pi^2*xi^2*HPL[{-1, 0, 0}, x] - 551880*xi^3*HPL[{-1, 0, 0}, x] - 252000*Pi^2*xi^3*HPL[{-1, 0, 0}, x] + 171360*Pi^2*xi^4*HPL[{-1, 0, 0}, x] - 241920*xi^5*HPL[{-1, 0, 0}, x] + 171360*Pi^2*xi^5*HPL[{-1, 0, 0}, x] - 40320*Pi^2*xi^6*HPL[{-1, 0, 0}, x] + 279720*xi^7*HPL[{-1, 0, 0}, x] - 30240*Pi^2*xi^7*HPL[{-1, 0, 0}, x] - 22680*xi^9*HPL[{-1, 0, 0}, x] + 1209600*xi*HPL[{-1, 1, -1}, x] - 2177280*xi^3*HPL[{-1, 1, -1}, x] + 1209600*xi^5*HPL[{-1, 1, -1}, x] - 241920*xi^7*HPL[{-1, 1, -1}, x] - 90720*Pi^2*HPL[{-1, 1, 0}, x] + 221760*Pi^2*xi^2*HPL[{-1, 1, 0}, x] - 171360*Pi^2*xi^4*HPL[{-1, 1, 0}, x] + 40320*Pi^2*xi^6*HPL[{-1, 1, 0}, x] + 1209600*xi*HPL[{-1, 1, 1}, x] - 2177280*xi^3*HPL[{-1, 1, 1}, x] + 1209600*xi^5*HPL[{-1, 1, 1}, x] - 241920*xi^7*HPL[{-1, 1, 1}, x] + 64260*HPL[{0, 0, 0}, x] - 36540*Pi^2*HPL[{0, 0, 0}, x] - 574560*xi*HPL[{0, 0, 0}, x] - 254520*Pi^2*xi*HPL[{0, 0, 0}, x] - 854280*xi^2*HPL[{0, 0, 0}, x] + 68040*Pi^2*xi^2*HPL[{0, 0, 0}, x] + 574560*xi^3*HPL[{0, 0, 0}, x] + 582120*Pi^2*xi^3*HPL[{0, 0, 0}, x] + 1304100*xi^4*HPL[{0, 0, 0}, x] - 22680*Pi^2*xi^4*HPL[{0, 0, 0}, x] + 272160*xi^5*HPL[{0, 0, 0}, x] - 400680*Pi^2*xi^5*HPL[{0, 0, 0}, x] - 529200*xi^6*HPL[{0, 0, 0}, x] - 12600*Pi^2*xi^6*HPL[{0, 0, 0}, x] - 302400*xi^7*HPL[{0, 0, 0}, x] + 73080*Pi^2*xi^7*HPL[{0, 0, 0}, x] + 15120*xi^8*HPL[{0, 0, 0}, x] + 3780*Pi^2*xi^8*HPL[{0, 0, 0}, x] + 30240*xi^9*HPL[{0, 0, 0}, x] - 544320*HPL[{1, -3, 0}, x] + 1330560*xi^2*HPL[{1, -3, 0}, x] - 1028160*xi^4*HPL[{1, -3, 0}, x] + 241920*xi^6*HPL[{1, -3, 0}, x] + 1209600*xi*HPL[{1, -1, -1}, x] - 2177280*xi^3*HPL[{1, -1, -1}, x] + 1209600*xi^5*HPL[{1, -1, -1}, x] - 241920*xi^7*HPL[{1, -1, -1}, x] - 90720*Pi^2*HPL[{1, -1, 0}, x] + 221760*Pi^2*xi^2*HPL[{1, -1, 0}, x] - 171360*Pi^2*xi^4*HPL[{1, -1, 0}, x] + 40320*Pi^2*xi^6*HPL[{1, -1, 0}, x] + 1209600*xi*HPL[{1, -1, 1}, x] - 2177280*xi^3*HPL[{1, -1, 1}, x] + 1209600*xi^5*HPL[{1, -1, 1}, x] - 241920*xi^7*HPL[{1, -1, 1}, x] + 90720*Pi^2*HPL[{1, 0, 0}, x] + 294840*xi*HPL[{1, 0, 0}, x] + 50400*Pi^2*xi*HPL[{1, 0, 0}, x] - 221760*Pi^2*xi^2*HPL[{1, 0, 0}, x] - 551880*xi^3*HPL[{1, 0, 0}, x] - 110880*Pi^2*xi^3*HPL[{1, 0, 0}, x] + 171360*Pi^2*xi^4*HPL[{1, 0, 0}, x] + 302400*xi^5*HPL[{1, 0, 0}, x] + 70560*Pi^2*xi^5*HPL[{1, 0, 0}, x] - 40320*Pi^2*xi^6*HPL[{1, 0, 0}, x] - 52920*xi^7*HPL[{1, 0, 0}, x] - 10080*Pi^2*xi^7*HPL[{1, 0, 0}, x] + 7560*xi^9*HPL[{1, 0, 0}, x] + 1209600*xi*HPL[{1, 1, -1}, x] - 2177280*xi^3*HPL[{1, 1, -1}, x] + 1209600*xi^5*HPL[{1, 1, -1}, x] - 241920*xi^7*HPL[{1, 1, -1}, x] - 90720*Pi^2*HPL[{1, 1, 0}, x] + 221760*Pi^2*xi^2*HPL[{1, 1, 0}, x] - 171360*Pi^2*xi^4*HPL[{1, 1, 0}, x] + 40320*Pi^2*xi^6*HPL[{1, 1, 0}, x] + 1209600*xi*HPL[{1, 1, 1}, x] - 2177280*xi^3*HPL[{1, 1, 1}, x] + 1209600*xi^5*HPL[{1, 1, 1}, x] - 241920*xi^7*HPL[{1, 1, 1}, x] - 45360*HPL[{2, 0, 0}, x] + 40320*Pi^2*HPL[{2, 0, 0}, x] + 136080*xi*HPL[{2, 0, 0}, x] + 30240*xi^2*HPL[{2, 0, 0}, x] - 100800*Pi^2*xi^2*HPL[{2, 0, 0}, x] - 287280*xi^3*HPL[{2, 0, 0}, x] + 75600*xi^4*HPL[{2, 0, 0}, x] + 80640*Pi^2*xi^4*HPL[{2, 0, 0}, x] + 181440*xi^5*HPL[{2, 0, 0}, x] - 75600*xi^6*HPL[{2, 0, 0}, x] - 20160*Pi^2*xi^6*HPL[{2, 0, 0}, x] - 30240*xi^7*HPL[{2, 0, 0}, x] + 15120*xi^8*HPL[{2, 0, 0}, x] + 68040*HPL[{3, 0, 0}, x] - 166320*xi*HPL[{3, 0, 0}, x] - 166320*xi^2*HPL[{3, 0, 0}, x] + 378000*xi^3*HPL[{3, 0, 0}, x] + 128520*xi^4*HPL[{3, 0, 0}, x] - 257040*xi^5*HPL[{3, 0, 0}, x] - 30240*xi^6*HPL[{3, 0, 0}, x] + 45360*xi^7*HPL[{3, 0, 0}, x] - 105840*HPL[{4, 0, 0}, x] + 272160*xi^2*HPL[{4, 0, 0}, x] - 226800*xi^4*HPL[{4, 0, 0}, x] + 60480*xi^6*HPL[{4, 0, 0}, x] + 423360*HPL[{-3, 0, 0, 0}, x] - 1088640*xi^2*HPL[{-3, 0, 0, 0}, x] + 907200*xi^4*HPL[{-3, 0, 0, 0}, x] - 241920*xi^6*HPL[{-3, 0, 0, 0}, x] - 544320*HPL[{-2, -1, 0, 0}, x] + 1330560*xi^2*HPL[{-2, -1, 0, 0}, x] - 1028160*xi^4*HPL[{-2, -1, 0, 0}, x] + 241920*xi^6*HPL[{-2, -1, 0, 0}, x] + 408240*HPL[{-2, 0, 0, 0}, x] + 665280*xi*HPL[{-2, 0, 0, 0}, x] - 997920*xi^2*HPL[{-2, 0, 0, 0}, x] - 1512000*xi^3*HPL[{-2, 0, 0, 0}, x] + 771120*xi^4*HPL[{-2, 0, 0, 0}, x] + 1028160*xi^5*HPL[{-2, 0, 0, 0}, x] - 181440*xi^6*HPL[{-2, 0, 0, 0}, x] - 181440*xi^7*HPL[{-2, 0, 0, 0}, x] - 272160*HPL[{-2, 1, 0, 0}, x] + 665280*xi^2*HPL[{-2, 1, 0, 0}, x] - 514080*xi^4*HPL[{-2, 1, 0, 0}, x] + 120960*xi^6*HPL[{-2, 1, 0, 0}, x] - 544320*HPL[{-1, -2, 0, 0}, x] + 1330560*xi^2*HPL[{-1, -2, 0, 0}, x] - 1028160*xi^4*HPL[{-1, -2, 0, 0}, x] + 241920*xi^6*HPL[{-1, -2, 0, 0}, x] - 1088640*xi*HPL[{-1, -1, 0, 0}, x] + 2298240*xi^3*HPL[{-1, -1, 0, 0}, x] - 1451520*xi^5*HPL[{-1, -1, 0, 0}, x] + 241920*xi^7*HPL[{-1, -1, 0, 0}, x] - 60480*HPL[{-1, 0, 0, 0}, x] + 70560*Pi^2*HPL[{-1, 0, 0, 0}, x] + 816480*xi*HPL[{-1, 0, 0, 0}, x] + 665280*xi^2*HPL[{-1, 0, 0, 0}, x] - 181440*Pi^2*xi^2*HPL[{-1, 0, 0, 0}, x] - 1723680*xi^3*HPL[{-1, 0, 0, 0}, x] - 1149120*xi^4*HPL[{-1, 0, 0, 0}, x] + 151200*Pi^2*xi^4*HPL[{-1, 0, 0, 0}, x] + 1088640*xi^5*HPL[{-1, 0, 0, 0}, x] + 604800*xi^6*HPL[{-1, 0, 0, 0}, x] - 40320*Pi^2*xi^6*HPL[{-1, 0, 0, 0}, x] - 181440*xi^7*HPL[{-1, 0, 0, 0}, x] - 60480*xi^8*HPL[{-1, 0, 0, 0}, x] - 544320*xi*HPL[{-1, 1, 0, 0}, x] + 1149120*xi^3*HPL[{-1, 1, 0, 0}, x] - 725760*xi^5*HPL[{-1, 1, 0, 0}, x] + 120960*xi^7*HPL[{-1, 1, 0, 0}, x] - 272160*HPL[{-1, 2, 0, 0}, x] + 665280*xi^2*HPL[{-1, 2, 0, 0}, x] - 514080*xi^4*HPL[{-1, 2, 0, 0}, x] + 120960*xi^6*HPL[{-1, 2, 0, 0}, x] + 52920*HPL[{0, 0, 0, 0}, x] - 153720*Pi^2*HPL[{0, 0, 0, 0}, x] - 718200*xi*HPL[{0, 0, 0, 0}, x] - 1134000*xi^2*HPL[{0, 0, 0, 0}, x] + 398160*Pi^2*xi^2*HPL[{0, 0, 0, 0}, x] + 1247400*xi^3*HPL[{0, 0, 0, 0}, x] + 2109240*xi^4*HPL[{0, 0, 0, 0}, x] - 335160*Pi^2*xi^4*HPL[{0, 0, 0, 0}, x] - 438480*xi^5*HPL[{0, 0, 0, 0}, x] - 1171800*xi^6*HPL[{0, 0, 0, 0}, x] + 90720*Pi^2*xi^6*HPL[{0, 0, 0, 0}, x] - 105840*xi^7*HPL[{0, 0, 0, 0}, x] + 143640*xi^8*HPL[{0, 0, 0, 0}, x] + 15120*xi^9*HPL[{0, 0, 0, 0}, x] - 544320*HPL[{1, -2, 0, 0}, x] + 1330560*xi^2*HPL[{1, -2, 0, 0}, x] - 1028160*xi^4*HPL[{1, -2, 0, 0}, x] + 241920*xi^6*HPL[{1, -2, 0, 0}, x] - 544320*xi*HPL[{1, -1, 0, 0}, x] + 1149120*xi^3*HPL[{1, -1, 0, 0}, x] - 725760*xi^5*HPL[{1, -1, 0, 0}, x] + 120960*xi^7*HPL[{1, -1, 0, 0}, x] - 60480*HPL[{1, 0, 0, 0}, x] + 70560*Pi^2*HPL[{1, 0, 0, 0}, x] + 136080*xi*HPL[{1, 0, 0, 0}, x] + 423360*xi^2*HPL[{1, 0, 0, 0}, x] - 181440*Pi^2*xi^2*HPL[{1, 0, 0, 0}, x] - 287280*xi^3*HPL[{1, 0, 0, 0}, x] - 665280*xi^4*HPL[{1, 0, 0, 0}, x] + 151200*Pi^2*xi^4*HPL[{1, 0, 0, 0}, x] + 181440*xi^5*HPL[{1, 0, 0, 0}, x] + 332640*xi^6*HPL[{1, 0, 0, 0}, x] - 40320*Pi^2*xi^6*HPL[{1, 0, 0, 0}, x] - 30240*xi^7*HPL[{1, 0, 0, 0}, x] - 30240*xi^8*HPL[{1, 0, 0, 0}, x] - 272160*xi*HPL[{1, 1, 0, 0}, x] + 574560*xi^3*HPL[{1, 1, 0, 0}, x] - 362880*xi^5*HPL[{1, 1, 0, 0}, x] + 60480*xi^7*HPL[{1, 1, 0, 0}, x] - 272160*HPL[{1, 2, 0, 0}, x] + 665280*xi^2*HPL[{1, 2, 0, 0}, x] - 514080*xi^4*HPL[{1, 2, 0, 0}, x] + 120960*xi^6*HPL[{1, 2, 0, 0}, x] - 272160*HPL[{2, -1, 0, 0}, x] + 665280*xi^2*HPL[{2, -1, 0, 0}, x] - 514080*xi^4*HPL[{2, -1, 0, 0}, x] + 120960*xi^6*HPL[{2, -1, 0, 0}, x] + 68040*HPL[{2, 0, 0, 0}, x] + 332640*xi*HPL[{2, 0, 0, 0}, x] - 166320*xi^2*HPL[{2, 0, 0, 0}, x] - 756000*xi^3*HPL[{2, 0, 0, 0}, x] + 128520*xi^4*HPL[{2, 0, 0, 0}, x] + 514080*xi^5*HPL[{2, 0, 0, 0}, x] - 30240*xi^6*HPL[{2, 0, 0, 0}, x] - 90720*xi^7*HPL[{2, 0, 0, 0}, x] - 136080*HPL[{2, 1, 0, 0}, x] + 332640*xi^2*HPL[{2, 1, 0, 0}, x] - 257040*xi^4*HPL[{2, 1, 0, 0}, x] + 60480*xi^6*HPL[{2, 1, 0, 0}, x] + 211680*HPL[{3, 0, 0, 0}, x] - 544320*xi^2*HPL[{3, 0, 0, 0}, x] + 453600*xi^4*HPL[{3, 0, 0, 0}, x] - 120960*xi^6*HPL[{3, 0, 0, 0}, x] + 604800*HPL[{-2, 0, 0, 0, 0}, x] - 1572480*xi^2*HPL[{-2, 0, 0, 0, 0}, x] + 1330560*xi^4*HPL[{-2, 0, 0, 0, 0}, x] - 362880*xi^6*HPL[{-2, 0, 0, 0, 0}, x] - 544320*HPL[{-1, -1, 0, 0, 0}, x] + 1330560*xi^2*HPL[{-1, -1, 0, 0, 0}, x] - 1028160*xi^4*HPL[{-1, -1, 0, 0, 0}, x] + 241920*xi^6*HPL[{-1, -1, 0, 0, 0}, x] + 408240*HPL[{-1, 0, 0, 0, 0}, x] + 1028160*xi*HPL[{-1, 0, 0, 0, 0}, x] - 997920*xi^2*HPL[{-1, 0, 0, 0, 0}, x] - 2358720*xi^3*HPL[{-1, 0, 0, 0, 0}, x] + 771120*xi^4*HPL[{-1, 0, 0, 0, 0}, x] + 1632960*xi^5*HPL[{-1, 0, 0, 0, 0}, x] - 181440*xi^6*HPL[{-1, 0, 0, 0, 0}, x] - 302400*xi^7*HPL[{-1, 0, 0, 0, 0}, x] - 544320*HPL[{-1, 1, 0, 0, 0}, x] + 1330560*xi^2*HPL[{-1, 1, 0, 0, 0}, x] - 1028160*xi^4*HPL[{-1, 1, 0, 0, 0}, x] + 241920*xi^6*HPL[{-1, 1, 0, 0, 0}, x] + 56700*HPL[{0, 0, 0, 0, 0}, x] - 1489320*xi*HPL[{0, 0, 0, 0, 0}, x] - 340200*xi^2*HPL[{0, 0, 0, 0, 0}, x] + 3439800*xi^3*HPL[{0, 0, 0, 0, 0}, x] + 548100*xi^4*HPL[{0, 0, 0, 0, 0}, x] - 2411640*xi^5*HPL[{0, 0, 0, 0, 0}, x] - 302400*xi^6*HPL[{0, 0, 0, 0, 0}, x] + 461160*xi^7*HPL[{0, 0, 0, 0, 0}, x] + 37800*xi^8*HPL[{0, 0, 0, 0, 0}, x] - 544320*HPL[{1, -1, 0, 0, 0}, x] + 1330560*xi^2*HPL[{1, -1, 0, 0, 0}, x] - 1028160*xi^4*HPL[{1, -1, 0, 0, 0}, x] + 241920*xi^6*HPL[{1, -1, 0, 0, 0}, x] + 408240*HPL[{1, 0, 0, 0, 0}, x] + 302400*xi*HPL[{1, 0, 0, 0, 0}, x] - 997920*xi^2*HPL[{1, 0, 0, 0, 0}, x] - 665280*xi^3*HPL[{1, 0, 0, 0, 0}, x] + 771120*xi^4*HPL[{1, 0, 0, 0, 0}, x] + 423360*xi^5*HPL[{1, 0, 0, 0, 0}, x] - 181440*xi^6*HPL[{1, 0, 0, 0, 0}, x] - 60480*xi^7*HPL[{1, 0, 0, 0, 0}, x] - 544320*HPL[{1, 1, 0, 0, 0}, x] + 1330560*xi^2*HPL[{1, 1, 0, 0, 0}, x] - 1028160*xi^4*HPL[{1, 1, 0, 0, 0}, x] + 241920*xi^6*HPL[{1, 1, 0, 0, 0}, x] + 241920*HPL[{2, 0, 0, 0, 0}, x] - 604800*xi^2*HPL[{2, 0, 0, 0, 0}, x] + 483840*xi^4*HPL[{2, 0, 0, 0, 0}, x] - 120960*xi^6*HPL[{2, 0, 0, 0, 0}, x] + 604800*HPL[{-1, 0, 0, 0, 0, 0}, x] - 1572480*xi^2*HPL[{-1, 0, 0, 0, 0, 0}, x] + 1330560*xi^4*HPL[{-1, 0, 0, 0, 0, 0}, x] - 362880*xi^6*HPL[{-1, 0, 0, 0, 0, 0}, x] - 824040*HPL[{0, 0, 0, 0, 0, 0}, x] + 2162160*xi^2*HPL[{0, 0, 0, 0, 0, 0}, x] - 1852200*xi^4*HPL[{0, 0, 0, 0, 0, 0}, x] + 514080*xi^6*HPL[{0, 0, 0, 0, 0, 0}, x] + 604800*HPL[{1, 0, 0, 0, 0, 0}, x] - 1572480*xi^2*HPL[{1, 0, 0, 0, 0, 0}, x] + 1330560*xi^4*HPL[{1, 0, 0, 0, 0, 0}, x] - 362880*xi^6*HPL[{1, 0, 0, 0, 0, 0}, x] + 11340*Pi^2*Zeta[3] - 18900*xi*Zeta[3] - 12600*Pi^2*xi*Zeta[3] - 27720*Pi^2*xi^2*Zeta[3] + 11340*xi^3*Zeta[3] + 27720*Pi^2*xi^3*Zeta[3] + 21420*Pi^2*xi^4*Zeta[3] + 30240*xi^5*Zeta[3] - 17640*Pi^2*xi^5*Zeta[3] - 5040*Pi^2*xi^6*Zeta[3] - 26460*xi^7*Zeta[3] + 2520*Pi^2*xi^7*Zeta[3] + 3780*xi^9*Zeta[3] - 7560*HPL[{0}, x]*Zeta[3] - 10080*Pi^2*HPL[{0}, x]*Zeta[3] - 90720*xi^2*HPL[{0}, x]*Zeta[3] + 25200*Pi^2*xi^2*HPL[{0}, x]*Zeta[3] + 204120*xi^4*HPL[{0}, x]*Zeta[3] - 20160*Pi^2*xi^4*HPL[{0}, x]*Zeta[3] - 120960*xi^6*HPL[{0}, x]*Zeta[3] + 5040*Pi^2*xi^6*HPL[{0}, x]*Zeta[3] + 15120*xi^8*HPL[{0}, x]*Zeta[3] - 166320*xi*HPL[{0, 0}, x]*Zeta[3] + 378000*xi^3*HPL[{0, 0}, x]*Zeta[3] - 257040*xi^5*HPL[{0, 0}, x]*Zeta[3] + 45360*xi^7*HPL[{0, 0}, x]*Zeta[3] - 105840*HPL[{0, 0, 0}, x]*Zeta[3] + 272160*xi^2*HPL[{0, 0, 0}, x]*Zeta[3] - 226800*xi^4*HPL[{0, 0, 0}, x]*Zeta[3] + 60480*xi^6*HPL[{0, 0, 0}, x]*Zeta[3] + 34020*Zeta[5] - 154980*xi*Zeta[5] - 83160*xi^2*Zeta[5] + 359100*xi^3*Zeta[5] + 64260*xi^4*Zeta[5] - 253260*xi^5*Zeta[5] - 15120*xi^6*Zeta[5] + 49140*xi^7*Zeta[5] - 83160*HPL[{0}, x]*Zeta[5] + 219240*xi^2*HPL[{0}, x]*Zeta[5] - 189000*xi^4*HPL[{0}, x]*Zeta[5] + 52920*xi^6*HPL[{0}, x]*Zeta[5]))/(945*xi^3*(-1 + xi^2)^2)) ); (* -------------------------------- *) (* ---- High Energy Expansion ----- *) (* -------------------------------- *) (* Variables: R = u/v, rho = (u+v)/4 *) (* Leading and sub-leading term in the high energy expansion of the amplitude M with rho as expansion parameter. *) M[HE]=( 1 + g^2*(Pi^2 + 2*HPL[{-1}, R]*HPL[{0}, R] - 4*HPL[{-1, -1}, R] + (4*HPL[{-1}, R] - 2*HPL[{0}, R])*Log[rho] - 2*Log[rho]^2 + rho*(-2*(4 + Pi^2 + 2*(-2 + (1 + R)^(-1))*HPL[{0}, R] + 2*HPL[{-1}, R]*(3 + HPL[{0}, R]) - 4*HPL[{-1, -1}, R]) + 4*(3 - 2*HPL[{-1}, R] + HPL[{0}, R])*Log[rho] + 4*Log[rho]^2)) +g^4*(Pi^4/5 + ((-8*Pi^2)/3 + 4*HPL[{0}, R]^2)*HPL[{-1, -1}, R] - 24*HPL[{0}, R]*HPL[{-1, -1, -1}, R] + 48*HPL[{-1, -1, -1, -1}, R] + ((-4*Pi^2)/3 - 12*HPL[{-1}, R]*HPL[{0}, R] + 2*HPL[{0}, R]^2 + 24*HPL[{-1, -1}, R])*Log[rho]^2 + (-8*HPL[{-1}, R] + 4*HPL[{0}, R])*Log[rho]^3 + 2*Log[rho]^4 - 4*HPL[{0}, R]*Zeta[3] + (4*HPL[{-1}, R]*(Pi^2*HPL[{0}, R] + 6*Zeta[3]))/3 + (4*Log[rho]*(HPL[{-1}, R]*(2*Pi^2 - 3*HPL[{0}, R]^2) - HPL[{0}, R]*(Pi^2 - 18*HPL[{-1, -1}, R]) - 6*(6*HPL[{-1, -1, -1}, R] + Zeta[3])))/3 + rho*(16 - 8*Pi^2 + (8*Pi^4)/15 - (34*Pi^4)/(15*(1 + R)) + 48*(-1 + 2/(1 + R))*HPL[{-4}, R] - 8*Pi^2*HPL[{-2}, R] + (16*Pi^2*HPL[{-2}, R])/(1 + R) + (8*Pi^2*HPL[{-1}, R])/3 - (16*Pi^2*HPL[{0}, R])/3 + (8*Pi^2*HPL[{0}, R])/(1 + R) - 32*HPL[{-2}, R]*HPL[{0}, R] - (16*HPL[{-1}, R]*HPL[{0}, R])/(1 + R) - (8*Pi^2*HPL[{-1}, R]*HPL[{0}, R])/(1 + R) - 8*HPL[{0}, R]^2 + (8*HPL[{0}, R]^2)/(1 + R) - 8*HPL[{-2}, R]*HPL[{0}, R]^2 + (16*HPL[{-2}, R]*HPL[{0}, R]^2)/(1 + R) + 16*HPL[{-1}, R]*HPL[{0}, R]^2 + (8*HPL[{-1}, R]*HPL[{0}, R]^2)/(1 + R) + 32*HPL[{-3}, R]*(1 + (1 - 2/(1 + R))*HPL[{0}, R]) + 16*HPL[{-1, -1}, R] + 8*Pi^2*HPL[{-1, -1}, R] - 48*HPL[{0}, R]*HPL[{-1, -1}, R] - (16*HPL[{0}, R]*HPL[{-1, -1}, R])/(1 + R) - 8*HPL[{0}, R]^2*HPL[{-1, -1}, R] - (8*HPL[{0}, R]^2*HPL[{-1, -1}, R])/(1 + R) + 112*HPL[{-1, -1, -1}, R] + 64*HPL[{0}, R]*HPL[{-1, -1, -1}, R] + (16*HPL[{0}, R]*HPL[{-1, -1, -1}, R])/(1 + R) - 144*HPL[{-1, -1, -1, -1}, R] + 4*(2 + Pi^2 - 2*(3 + (1 + R)^(-1))*HPL[{0}, R] - (1 + (1 + R)^(-1))*HPL[{0}, R]^2 + 2*HPL[{-1}, R]*(7 + (4 + (1 + R)^(-1))*HPL[{0}, R]) - 18*HPL[{-1, -1}, R])* Log[rho]^2 + (8*(-7 + 9*HPL[{-1}, R] - (4 + (1 + R)^(-1))*HPL[{0}, R])*Log[rho]^3)/3 - 6*Log[rho]^4 + 24*Zeta[3] - 24*HPL[{-1}, R]*Zeta[3] + 8*HPL[{0}, R]*Zeta[3] + (8*HPL[{0}, R]*Zeta[3])/(1 + R) + (8*Log[rho]*(5*Pi^2 - (3*HPL[{0}, R]^2)/(1 + R) + 3*HPL[{-1}, R]*(-2 - Pi^2 + 2*(3 + (1 + R)^(-1))*HPL[{0}, R] + (1 + (1 + R)^(-1))*HPL[{0}, R]^2) - 42*HPL[{-1, -1}, R] + 3*HPL[{0}, R]*((2 + Pi^2)/(1 + R) - 2*(4 + (1 + R)^(-1))*HPL[{-1, -1}, R]) + 54*HPL[{-1, -1, -1}, R] + 9*Zeta[3]))/3)) + g^6*((11*Pi^6)/189 - 8*Pi^2*HPL[{0}, R]*HPL[{-1, -1, -1}, R] + 8*HPL[{0}, R]^3*HPL[{-1, -1, -1}, R] + 16*Pi^2*HPL[{-1, -1, -1, -1}, R] - 96*HPL[{0}, R]^2*HPL[{-1, -1, -1, -1}, R] + 480*HPL[{0}, R]*HPL[{-1, -1, -1, -1, -1}, R] - 960*HPL[{-1, -1, -1, -1, -1, -1}, R] + (2*(Pi^2 + 30*HPL[{-1}, R]*HPL[{0}, R] - 6*HPL[{0}, R]^2 - 60*HPL[{-1, -1}, R])*Log[rho]^4)/3 + (8*HPL[{-1}, R] - 4*HPL[{0}, R])*Log[rho]^5 - (4*Log[rho]^6)/3 - (16*Pi^2*HPL[{0}, R]*Zeta[3])/3 - 96*HPL[{-1, -1, -1}, R]*Zeta[3] - 16*Zeta[3]^2 - (4*HPL[{-1, -1}, R]*(Pi^4 - 3*Pi^2*HPL[{0}, R]^2 - 108*HPL[{0}, R]*Zeta[3]))/9 - (4*Log[rho]^3*(HPL[{0}, R]^3 + 2*HPL[{-1}, R]*(Pi^2 - 6*HPL[{0}, R]^2) - HPL[{0}, R]*(Pi^2 - 60*HPL[{-1, -1}, R]) - 12*(10*HPL[{-1, -1, -1}, R] + Zeta[3])))/3 + Log[rho]^2*((-2*Pi^4)/9 + (2*HPL[{0}, R]^2*(Pi^2 - 72*HPL[{-1, -1}, R]))/3 + 8*Pi^2*HPL[{-1, -1}, R] - 480*HPL[{-1, -1, -1, -1}, R] + 24*HPL[{0}, R]*(10*HPL[{-1, -1, -1}, R] + Zeta[3]) - 4*HPL[{-1}, R]*(Pi^2*HPL[{0}, R] - HPL[{0}, R]^3 + 12*Zeta[3])) + (2*HPL[{-1}, R]*(Pi^4*HPL[{0}, R] + 48*Pi^2*Zeta[3] - 36*HPL[{0}, R]^2*Zeta[3] - 324*Zeta[5]))/9 + 36*HPL[{0}, R]*Zeta[5] + Log[rho]*(-8*HPL[{0}, R]^3*HPL[{-1, -1}, R] - 16*Pi^2*HPL[{-1, -1, -1}, R] + HPL[{0}, R]*((-2*Pi^4)/9 + 8*Pi^2*HPL[{-1, -1}, R] - 480*HPL[{-1, -1, -1, -1}, R]) + 960*HPL[{-1, -1, -1, -1, -1}, R] - (32*Pi^2*Zeta[3])/3 + 96*HPL[{-1, -1}, R]*Zeta[3] + 8*HPL[{0}, R]^2*(12*HPL[{-1, -1, -1}, R] + Zeta[3]) + (4*HPL[{-1}, R]*(Pi^4 - 3*Pi^2*HPL[{0}, R]^2 - 108*HPL[{0}, R]*Zeta[3]))/9 + 72*Zeta[5]) + rho*(-48 + (32*Pi^2)/3 - (136*Pi^4)/45 - (278*Pi^6)/945 - (44*Pi^6)/(315*(1 + R)) - 320*(-1 + 2/(1 + R))*HPL[{-6}, R] - 32*Pi^2*HPL[{-4}, R] + (32*Pi^2*HPL[{-4}, R])/(1 + R) + 32*Pi^2*HPL[{-3}, R] - (32*Pi^2*HPL[{-3}, R])/(1 + R) - (16*Pi^4*HPL[{-2}, R])/5 + (32*Pi^4*HPL[{-2}, R])/(5*(1 + R)) + (524*Pi^4*HPL[{-1}, R])/45 - (136*Pi^4*HPL[{-1}, R])/(15*(1 + R)) - (272*Pi^4*HPL[{0}, R])/45 + (292*Pi^4*HPL[{0}, R])/(45*(1 + R)) + 256*HPL[{-4}, R]*HPL[{0}, R] - (192*HPL[{-4}, R]*HPL[{0}, R])/(1 + R) + (64*Pi^2*HPL[{-3}, R]*HPL[{0}, R])/3 - (128*Pi^2*HPL[{-3}, R]*HPL[{0}, R])/(3*(1 + R)) - (64*Pi^2*HPL[{-2}, R]*HPL[{0}, R])/3 + 16*HPL[{-1}, R]*HPL[{0}, R] - (4*Pi^4*HPL[{-1}, R]*HPL[{0}, R])/9 + (16*HPL[{-1}, R]*HPL[{0}, R])/(1 + R) - (32*Pi^2*HPL[{-1}, R]*HPL[{0}, R])/(3*(1 + R)) - (104*Pi^4*HPL[{-1}, R]*HPL[{0}, R])/(45*(1 + R)) + 8*HPL[{0}, R]^2 - (16*Pi^2*HPL[{0}, R]^2)/3 + (88*Pi^4*HPL[{0}, R]^2)/45 - (8*HPL[{0}, R]^2)/(1 + R) + (16*Pi^2*HPL[{0}, R]^2)/(3*(1 + R)) - (88*Pi^4*HPL[{0}, R]^2)/(45*(1 + R)) + 64*HPL[{-4}, R]*HPL[{0}, R]^2 - (64*HPL[{-4}, R]*HPL[{0}, R]^2)/(1 + R) - 96*HPL[{-3}, R]*HPL[{0}, R]^2 + (96*HPL[{-3}, R]*HPL[{0}, R]^2)/(1 + R) - (32*Pi^2*HPL[{-2}, R]*HPL[{0}, R]^2)/3 + (64*Pi^2*HPL[{-2}, R]*HPL[{0}, R]^2)/(3*(1 + R)) + (32*Pi^2*HPL[{-1}, R]*HPL[{0}, R]^2)/3 + (40*Pi^2*HPL[{-1}, R]*HPL[{0}, R]^2)/(3*(1 + R)) - (64*Pi^2*HPL[{0}, R]^3)/9 + (64*Pi^2*HPL[{0}, R]^3)/(9*(1 + R)) - (32*HPL[{-3}, R]*HPL[{0}, R]^3)/(3*(1 + R)) + (32*HPL[{-2}, R]*HPL[{0}, R]^3)/3 - (64*HPL[{-2}, R]*HPL[{0}, R]^3)/(3*(1 + R)) - 8*HPL[{-1}, R]*HPL[{0}, R]^3 + (16*Pi^2*HPL[{-1}, R]*HPL[{0}, R]^3)/9 + (8*HPL[{-1}, R]*HPL[{0}, R]^3)/(1 + R) - (16*Pi^2*HPL[{-1}, R]*HPL[{0}, R]^3)/(9*(1 + R)) - 2*HPL[{0}, R]^4 + (4*Pi^2*HPL[{0}, R]^4)/9 + (2*HPL[{0}, R]^4)/(1 + R) - (4*Pi^2*HPL[{0}, R]^4)/(9*(1 + R)) - (8*HPL[{-2}, R]*HPL[{0}, R]^4)/3 + (16*HPL[{-2}, R]*HPL[{0}, R]^4)/(3*(1 + R)) + (8*HPL[{-1}, R]*HPL[{0}, R]^4)/3 + (8*HPL[{-1}, R]*HPL[{0}, R]^4)/(3*(1 + R)) - (8*HPL[{0}, R]^5)/15 + (8*HPL[{0}, R]^5)/(15*(1 + R)) + (2*HPL[{-1}, R]*HPL[{0}, R]^5)/15 - (2*HPL[{-1}, R]*HPL[{0}, R]^5)/(15*(1 + R)) + HPL[{0}, R]^6/45 - HPL[{0}, R]^6/(45*(1 + R)) + 128*HPL[{-5}, R]*(-2 + (1 + R)^(-1) + (-2 + 3/(1 + R))*HPL[{0}, R]) + 256*HPL[{-5, -1}, R] - (128*HPL[{-5, -1}, R])/(1 + R) + 64*HPL[{-4, -2}, R] + (64*HPL[{-4, -2}, R])/(1 + R) - 320*HPL[{-4, -1}, R] + (384*HPL[{-4, -1}, R])/(1 + R) - 192*HPL[{0}, R]*HPL[{-4, -1}, R] + (192*HPL[{0}, R]*HPL[{-4, -1}, R])/(1 + R) + 128*HPL[{-3, -3}, R] + (64*HPL[{-3, -3}, R])/(1 + R) - 64*HPL[{-3, -2}, R] + (128*HPL[{-3, -2}, R])/(1 + R) - 64*HPL[{0}, R]*HPL[{-3, -2}, R] + (32*Pi^2*HPL[{-3, -1}, R])/(1 + R) + 256*HPL[{0}, R]*HPL[{-3, -1}, R] - (256*HPL[{0}, R]*HPL[{-3, -1}, R])/(1 + R) + 64*HPL[{0}, R]^2*HPL[{-3, -1}, R] - (96*HPL[{0}, R]^2*HPL[{-3, -1}, R])/(1 + R) + 192*HPL[{-2, -4}, R] - 128*HPL[{-2, -3}, R] + (256*HPL[{-2, -3}, R])/(1 + R) - 128*HPL[{0}, R]*HPL[{-2, -3}, R] + (64*HPL[{0}, R]*HPL[{-2, -3}, R])/(1 + R) + (32*Pi^2*HPL[{-2, -2}, R])/(1 + R) + 64*HPL[{0}, R]*HPL[{-2, -2}, R] - (128*HPL[{0}, R]*HPL[{-2, -2}, R])/(1 + R) + 32*HPL[{0}, R]^2*HPL[{-2, -2}, R] - (32*HPL[{0}, R]^2*HPL[{-2, -2}, R])/(1 + R) - 32*Pi^2*HPL[{-2, -1}, R] + (64*Pi^2*HPL[{-2, -1}, R])/(1 + R) - 96*HPL[{0}, R]^2*HPL[{-2, -1}, R] + (64*HPL[{0}, R]^2*HPL[{-2, -1}, R])/(1 + R) - (32*HPL[{0}, R]^3*HPL[{-2, -1}, R])/3 + (64*HPL[{0}, R]^3*HPL[{-2, -1}, R])/(3*(1 + R)) + 256*HPL[{-1, -5}, R] - (128*HPL[{-1, -5}, R])/(1 + R) - 192*HPL[{-1, -4}, R] + (384*HPL[{-1, -4}, R])/(1 + R) - 192*HPL[{0}, R]*HPL[{-1, -4}, R] + (192*HPL[{0}, R]*HPL[{-1, -4}, R])/(1 + R) + (32*Pi^2*HPL[{-1, -3}, R])/(1 + R) + 128*HPL[{0}, R]*HPL[{-1, -3}, R] - (256*HPL[{0}, R]*HPL[{-1, -3}, R])/(1 + R) + 64*HPL[{0}, R]^2*HPL[{-1, -3}, R] - (96*HPL[{0}, R]^2*HPL[{-1, -3}, R])/(1 + R) - 32*Pi^2*HPL[{-1, -2}, R] + (64*Pi^2*HPL[{-1, -2}, R])/(1 + R) - 32*HPL[{0}, R]^2*HPL[{-1, -2}, R] + (64*HPL[{0}, R]^2*HPL[{-1, -2}, R])/(1 + R) - (32*HPL[{0}, R]^3*HPL[{-1, -2}, R])/3 + (64*HPL[{0}, R]^3*HPL[{-1, -2}, R])/(3*(1 + R)) - 48*HPL[{-1, -1}, R] + (32*Pi^2*HPL[{-1, -1}, R])/3 - (88*Pi^4*HPL[{-1, -1}, R])/15 + (136*Pi^4*HPL[{-1, -1}, R])/(15*(1 + R)) + 16*Pi^2*HPL[{0}, R]*HPL[{-1, -1}, R] - (176*Pi^2*HPL[{0}, R]*HPL[{-1, -1}, R])/(3*(1 + R)) + 40*HPL[{0}, R]^2*HPL[{-1, -1}, R] + (8*Pi^2*HPL[{0}, R]^2*HPL[{-1, -1}, R])/3 - (72*HPL[{0}, R]^2*HPL[{-1, -1}, R])/(1 + R) - (64*Pi^2*HPL[{0}, R]^2*HPL[{-1, -1}, R])/(3*(1 + R)) + (32*HPL[{0}, R]^3*HPL[{-1, -1}, R])/3 + (80*HPL[{0}, R]^3*HPL[{-1, -1}, R])/(3*(1 + R)) + (2*HPL[{0}, R]^4*HPL[{-1, -1}, R])/3 - (2*HPL[{0}, R]^4*HPL[{-1, -1}, R])/(3*(1 + R)) + 192*HPL[{-4, -1, -1}, R] - (384*HPL[{-4, -1, -1}, R])/(1 + R) + 64*HPL[{-3, -2, -1}, R] - (128*HPL[{-3, -2, -1}, R])/(1 + R) + 64*HPL[{-3, -1, -2}, R] - (128*HPL[{-3, -1, -2}, R])/(1 + R) - 128*HPL[{-3, -1, -1}, R] - 128*HPL[{0}, R]*HPL[{-3, -1, -1}, R] + (256*HPL[{0}, R]*HPL[{-3, -1, -1}, R])/(1 + R) + 128*HPL[{-2, -3, -1}, R] - (256*HPL[{-2, -3, -1}, R])/(1 + R) + 64*HPL[{-2, -2, -2}, R] - (128*HPL[{-2, -2, -2}, R])/(1 + R) - 64*HPL[{0}, R]*HPL[{-2, -2, -1}, R] + (128*HPL[{0}, R]*HPL[{-2, -2, -1}, R])/(1 + R) + 128*HPL[{-2, -1, -3}, R] - (256*HPL[{-2, -1, -3}, R])/(1 + R) - 64*HPL[{0}, R]*HPL[{-2, -1, -2}, R] + (128*HPL[{0}, R]*HPL[{-2, -1, -2}, R])/(1 + R) + 32*Pi^2*HPL[{-2, -1, -1}, R] - (64*Pi^2*HPL[{-2, -1, -1}, R])/(1 + R) + 128*HPL[{0}, R]*HPL[{-2, -1, -1}, R] + 32*HPL[{0}, R]^2*HPL[{-2, -1, -1}, R] - (64*HPL[{0}, R]^2*HPL[{-2, -1, -1}, R])/(1 + R) + 192*HPL[{-1, -4, -1}, R] - (384*HPL[{-1, -4, -1}, R])/(1 + R) + 64*HPL[{-1, -3, -2}, R] - (128*HPL[{-1, -3, -2}, R])/(1 + R) - 128*HPL[{0}, R]*HPL[{-1, -3, -1}, R] + (256*HPL[{0}, R]*HPL[{-1, -3, -1}, R])/(1 + R) + 128*HPL[{-1, -2, -3}, R] - (256*HPL[{-1, -2, -3}, R])/(1 + R) - 64*HPL[{0}, R]*HPL[{-1, -2, -2}, R] + (128*HPL[{0}, R]*HPL[{-1, -2, -2}, R])/(1 + R) + 32*Pi^2*HPL[{-1, -2, -1}, R] - (64*Pi^2*HPL[{-1, -2, -1}, R])/(1 + R) + 32*HPL[{0}, R]^2*HPL[{-1, -2, -1}, R] - (64*HPL[{0}, R]^2*HPL[{-1, -2, -1}, R])/(1 + R) + 192*HPL[{-1, -1, -4}, R] - (384*HPL[{-1, -1, -4}, R])/(1 + R) - 128*HPL[{0}, R]*HPL[{-1, -1, -3}, R] + (256*HPL[{0}, R]*HPL[{-1, -1, -3}, R])/(1 + R) + 32*Pi^2*HPL[{-1, -1, -2}, R] - (64*Pi^2*HPL[{-1, -1, -2}, R])/(1 + R) + 32*HPL[{0}, R]^2*HPL[{-1, -1, -2}, R] - (64*HPL[{0}, R]^2*HPL[{-1, -1, -2}, R])/(1 + R) + (80*Pi^2*HPL[{-1, -1, -1}, R])/3 - 48*HPL[{0}, R]*HPL[{-1, -1, -1}, R] - 16*Pi^2*HPL[{0}, R]*HPL[{-1, -1, -1}, R] + (144*HPL[{0}, R]*HPL[{-1, -1, -1}, R])/(1 + R) + (224*Pi^2*HPL[{0}, R]*HPL[{-1, -1, -1}, R])/(3*(1 + R)) - 80*HPL[{0}, R]^2*HPL[{-1, -1, -1}, R] - (224*HPL[{0}, R]^2*HPL[{-1, -1, -1}, R])/(1 + R) - (40*HPL[{0}, R]^3*HPL[{-1, -1, -1}, R])/3 - (104*HPL[{0}, R]^3*HPL[{-1, -1, -1}, R])/(3*(1 + R)) - 48*HPL[{-1, -1, -1, -1}, R] - (128*Pi^2*HPL[{-1, -1, -1, -1}, R])/3 + 640*HPL[{0}, R]*HPL[{-1, -1, -1, -1}, R] + (448*HPL[{0}, R]*HPL[{-1, -1, -1, -1}, R])/(1 + R) + 200*HPL[{0}, R]^2*HPL[{-1, -1, -1, -1}, R] + (248*HPL[{0}, R]^2*HPL[{-1, -1, -1, -1}, R])/(1 + R) - 1728*HPL[{-1, -1, -1, -1, -1}, R] - 1328*HPL[{0}, R]*HPL[{-1, -1, -1, -1, -1}, R] - (496*HPL[{0}, R]*HPL[{-1, -1, -1, -1, -1}, R])/(1 + R) + 3152*HPL[{-1, -1, -1, -1, -1, -1}, R] + ((24*(10 + 7/(1 + R))*HPL[{0}, R] + (75 + 93/(1 + R))*HPL[{0}, R]^2 - 6*HPL[{-1}, R]*(108 + (83 + 31/(1 + R))*HPL[{0}, R]) - 2*(9 + 8*Pi^2 - 591*HPL[{-1, -1}, R]))*Log[rho]^4)/9 + ((216 - 394*HPL[{-1}, R] + 2*(83 + 31/(1 + R))*HPL[{0}, R])*Log[rho]^5)/15 + (197*Log[rho]^6)/45 + (32*Pi^2*Zeta[3])/3 + (32*Pi^2*Zeta[3])/(1 + R) - (64*HPL[{-3}, R]*Zeta[3])/(1 + R) + 64*HPL[{-2}, R]*Zeta[3] - (128*HPL[{-2}, R]*Zeta[3])/(1 + R) - 32*HPL[{-1}, R]*Zeta[3] - (32*Pi^2*HPL[{-1}, R]*Zeta[3])/3 - (32*Pi^2*HPL[{-1}, R]*Zeta[3])/(1 + R) + (32*Pi^2*HPL[{0}, R]*Zeta[3])/3 + (32*HPL[{0}, R]*Zeta[3])/(1 + R) + (64*Pi^2*HPL[{0}, R]*Zeta[3])/(3*(1 + R)) + 32*HPL[{-1}, R]*HPL[{0}, R]*Zeta[3] + (96*HPL[{-1}, R]*HPL[{0}, R]*Zeta[3])/(1 + R) - (16*HPL[{0}, R]^2*Zeta[3])/(1 + R) + 16*HPL[{-1}, R]*HPL[{0}, R]^2*Zeta[3] + (32*HPL[{-1}, R]*HPL[{0}, R]^2*Zeta[3])/(1 + R) - 64*HPL[{-2, -1}, R]*Zeta[3] + (128*HPL[{-2, -1}, R]*Zeta[3])/(1 + R) - 64*HPL[{-1, -2}, R]*Zeta[3] + (128*HPL[{-1, -2}, R]*Zeta[3])/(1 + R) - 160*HPL[{-1, -1}, R]*Zeta[3] - 96*HPL[{0}, R]*HPL[{-1, -1}, R]*Zeta[3] - (128*HPL[{0}, R]*HPL[{-1, -1}, R]*Zeta[3])/(1 + R) + 320*HPL[{-1, -1, -1}, R]*Zeta[3] + 32*Zeta[3]^2 + (32*Zeta[3]^2)/(1 + R) + Log[rho]^2*(-24 + (16*Pi^2)/3 - (44*Pi^4)/15 + (68*Pi^4)/(15*(1 + R)) - 96*(-1 + 2/(1 + R))*HPL[{-4}, R] + 16*Pi^2*HPL[{-2}, R] - (32*Pi^2*HPL[{-2}, R])/(1 + R) + (40*Pi^2*HPL[{-1}, R])/3 + 8*Pi^2*HPL[{0}, R] - (88*Pi^2*HPL[{0}, R])/(3*(1 + R)) + 64*HPL[{-2}, R]*HPL[{0}, R] - 24*HPL[{-1}, R]*HPL[{0}, R] - 8*Pi^2*HPL[{-1}, R]*HPL[{0}, R] + (72*HPL[{-1}, R]*HPL[{0}, R])/(1 + R) + (112*Pi^2*HPL[{-1}, R]*HPL[{0}, R])/(3*(1 + R)) + 20*HPL[{0}, R]^2 + (4*Pi^2*HPL[{0}, R]^2)/3 - (36*HPL[{0}, R]^2)/(1 + R) - (32*Pi^2*HPL[{0}, R]^2)/(3*(1 + R)) + 16*HPL[{-2}, R]*HPL[{0}, R]^2 - (32*HPL[{-2}, R]*HPL[{0}, R]^2)/(1 + R) - 40*HPL[{-1}, R]*HPL[{0}, R]^2 - (112*HPL[{-1}, R]*HPL[{0}, R]^2)/(1 + R) - (16*HPL[{0}, R]^3)/3 + (40*HPL[{0}, R]^3)/(3*(1 + R)) - (20*HPL[{-1}, R]*HPL[{0}, R]^3)/3 - (52*HPL[{-1}, R]*HPL[{0}, R]^3)/(3*(1 + R)) + HPL[{0}, R]^4/3 - HPL[{0}, R]^4/(3*(1 + R)) + 64*HPL[{-3}, R]*(-1 + (-1 + 2/(1 + R))*HPL[{0}, R]) - 24*HPL[{-1, -1}, R] - (64*Pi^2*HPL[{-1, -1}, R])/3 + 320*HPL[{0}, R]*HPL[{-1, -1}, R] + (224*HPL[{0}, R]*HPL[{-1, -1}, R])/(1 + R) + 100*HPL[{0}, R]^2*HPL[{-1, -1}, R] + (124*HPL[{0}, R]^2*HPL[{-1, -1}, R])/(1 + R) - 864*HPL[{-1, -1, -1}, R] - 664*HPL[{0}, R]*HPL[{-1, -1, -1}, R] - (248*HPL[{0}, R]*HPL[{-1, -1, -1}, R])/(1 + R) + 1576*HPL[{-1, -1, -1, -1}, R] - 144*Zeta[3] + 160*HPL[{-1}, R]*Zeta[3] - 48*HPL[{0}, R]*Zeta[3] - (64*HPL[{0}, R]*Zeta[3])/(1 + R)) + (4*Log[rho]^3*((6 + 84/(1 + R))*HPL[{0}, R]^2 + (5 + 13/(1 + R))*HPL[{0}, R]^3 + HPL[{-1}, R]*(2*(9 + 8*Pi^2) - 24*(10 + 7/(1 + R))*HPL[{0}, R] - 3*(25 + 31/(1 + R))*HPL[{0}, R]^2) + HPL[{0}, R]*(18 - 54/(1 + R) + Pi^2*(6 - 28/(1 + R)) + 6*(83 + 31/(1 + R))*HPL[{-1, -1}, R]) - 2*(17*Pi^2 - 324*HPL[{-1, -1}, R] + 591*HPL[{-1, -1, -1}, R] + 60*Zeta[3])))/9 - 248*Zeta[5] + (64*Zeta[5])/(1 + R) + 256*HPL[{-1}, R]*Zeta[5] - (64*HPL[{-1}, R]*Zeta[5])/(1 + R) - 72*HPL[{0}, R]*Zeta[5] - (48*HPL[{0}, R]*Zeta[5])/(1 + R) + Log[rho]*((-236*Pi^4)/45 + (136*Pi^4)/(15*(1 + R)) + 128*(-2 + (1 + R)^(-1))*HPL[{-5}, R] - (32*Pi^2*HPL[{-3}, R])/(1 + R) + 32*Pi^2*HPL[{-2}, R] - (64*Pi^2*HPL[{-2}, R])/(1 + R) + 48*HPL[{-1}, R] - (32*Pi^2*HPL[{-1}, R])/3 + (88*Pi^4*HPL[{-1}, R])/15 - (136*Pi^4*HPL[{-1}, R])/(15*(1 + R)) - 16*HPL[{0}, R] + (4*Pi^4*HPL[{0}, R])/9 - (16*HPL[{0}, R])/(1 + R) + (32*Pi^2*HPL[{0}, R])/(3*(1 + R)) + (104*Pi^4*HPL[{0}, R])/(45*(1 + R)) - 256*HPL[{-3}, R]*HPL[{0}, R] + (256*HPL[{-3}, R]*HPL[{0}, R])/(1 + R) - 16*Pi^2*HPL[{-1}, R]*HPL[{0}, R] + (176*Pi^2*HPL[{-1}, R]*HPL[{0}, R])/(3*(1 + R)) + (32*Pi^2*HPL[{0}, R]^2)/3 - (40*Pi^2*HPL[{0}, R]^2)/(3*(1 + R)) - 64*HPL[{-3}, R]*HPL[{0}, R]^2 + (96*HPL[{-3}, R]*HPL[{0}, R]^2)/(1 + R) + 96*HPL[{-2}, R]*HPL[{0}, R]^2 - (64*HPL[{-2}, R]*HPL[{0}, R]^2)/(1 + R) - 40*HPL[{-1}, R]*HPL[{0}, R]^2 - (8*Pi^2*HPL[{-1}, R]*HPL[{0}, R]^2)/3 + (72*HPL[{-1}, R]*HPL[{0}, R]^2)/(1 + R) + (64*Pi^2*HPL[{-1}, R]*HPL[{0}, R]^2)/(3*(1 + R)) + 8*HPL[{0}, R]^3 - (16*Pi^2*HPL[{0}, R]^3)/9 - (8*HPL[{0}, R]^3)/(1 + R) + (16*Pi^2*HPL[{0}, R]^3)/(9*(1 + R)) + (32*HPL[{-2}, R]*HPL[{0}, R]^3)/3 - (64*HPL[{-2}, R]*HPL[{0}, R]^3)/(3*(1 + R)) - (32*HPL[{-1}, R]*HPL[{0}, R]^3)/3 - (80*HPL[{-1}, R]*HPL[{0}, R]^3)/(3*(1 + R)) + (8*HPL[{0}, R]^4)/3 - (8*HPL[{0}, R]^4)/(3*(1 + R)) - (2*HPL[{-1}, R]*HPL[{0}, R]^4)/3 + (2*HPL[{-1}, R]*HPL[{0}, R]^4)/(3*(1 + R)) - (2*HPL[{0}, R]^5)/15 + (2*HPL[{0}, R]^5)/(15*(1 + R)) - 64*HPL[{-4}, R]*(-5 + 6/(1 + R) + 3*(-1 + (1 + R)^(-1))*HPL[{0}, R]) - 192*HPL[{-4, -1}, R] + (384*HPL[{-4, -1}, R])/(1 + R) - 64*HPL[{-3, -2}, R] + (128*HPL[{-3, -2}, R])/(1 + R) + 128*HPL[{-3, -1}, R] + 128*HPL[{0}, R]*HPL[{-3, -1}, R] - (256*HPL[{0}, R]*HPL[{-3, -1}, R])/(1 + R) - 128*HPL[{-2, -3}, R] + (256*HPL[{-2, -3}, R])/(1 + R) + 64*HPL[{0}, R]*HPL[{-2, -2}, R] - (128*HPL[{0}, R]*HPL[{-2, -2}, R])/(1 + R) - 32*Pi^2*HPL[{-2, -1}, R] + (64*Pi^2*HPL[{-2, -1}, R])/(1 + R) - 128*HPL[{0}, R]*HPL[{-2, -1}, R] - 32*HPL[{0}, R]^2*HPL[{-2, -1}, R] + (64*HPL[{0}, R]^2*HPL[{-2, -1}, R])/(1 + R) - 192*HPL[{-1, -4}, R] + (384*HPL[{-1, -4}, R])/(1 + R) + 128*HPL[{0}, R]*HPL[{-1, -3}, R] - (256*HPL[{0}, R]*HPL[{-1, -3}, R])/(1 + R) - 32*Pi^2*HPL[{-1, -2}, R] + (64*Pi^2*HPL[{-1, -2}, R])/(1 + R) - 32*HPL[{0}, R]^2*HPL[{-1, -2}, R] + (64*HPL[{0}, R]^2*HPL[{-1, -2}, R])/(1 + R) - (80*Pi^2*HPL[{-1, -1}, R])/3 + 48*HPL[{0}, R]*HPL[{-1, -1}, R] + 16*Pi^2*HPL[{0}, R]*HPL[{-1, -1}, R] - (144*HPL[{0}, R]*HPL[{-1, -1}, R])/(1 + R) - (224*Pi^2*HPL[{0}, R]*HPL[{-1, -1}, R])/(3*(1 + R)) + 80*HPL[{0}, R]^2*HPL[{-1, -1}, R] + (224*HPL[{0}, R]^2*HPL[{-1, -1}, R])/(1 + R) + (40*HPL[{0}, R]^3*HPL[{-1, -1}, R])/3 + (104*HPL[{0}, R]^3*HPL[{-1, -1}, R])/(3*(1 + R)) + 48*HPL[{-1, -1, -1}, R] + (128*Pi^2*HPL[{-1, -1, -1}, R])/3 - 640*HPL[{0}, R]*HPL[{-1, -1, -1}, R] - (448*HPL[{0}, R]*HPL[{-1, -1, -1}, R])/(1 + R) - 200*HPL[{0}, R]^2*HPL[{-1, -1, -1}, R] - (248*HPL[{0}, R]^2*HPL[{-1, -1, -1}, R])/(1 + R) + 1728*HPL[{-1, -1, -1, -1}, R] + 1328*HPL[{0}, R]*HPL[{-1, -1, -1, -1}, R] + (496*HPL[{0}, R]*HPL[{-1, -1, -1, -1}, R])/(1 + R) - 3152*HPL[{-1, -1, -1, -1, -1}, R] + 32*Zeta[3] + (32*Pi^2*Zeta[3])/3 + (32*Pi^2*Zeta[3])/(1 + R) + 64*HPL[{-2}, R]*Zeta[3] - (128*HPL[{-2}, R]*Zeta[3])/(1 + R) + 160*HPL[{-1}, R]*Zeta[3] - 32*HPL[{0}, R]*Zeta[3] - (96*HPL[{0}, R]*Zeta[3])/(1 + R) + 96*HPL[{-1}, R]*HPL[{0}, R]*Zeta[3] + (128*HPL[{-1}, R]*HPL[{0}, R]*Zeta[3])/(1 + R) - 16*HPL[{0}, R]^2*Zeta[3] - (32*HPL[{0}, R]^2*Zeta[3])/(1 + R) - 320*HPL[{-1, -1}, R]*Zeta[3] - 256*Zeta[5] + (64*Zeta[5])/(1 + R)))) );