Ancillary file for:

The photon-energy spectrum in $B\to X_s\gamma$ to N$^3$LO:
light-fermion and large-$N_c$ corrections

Matteo Fael, Fabian Lange, Kay Sch\"onwald, Matthias Steinhauser

spectrum.m: 
    The result for the spectrum, first entry are the distributions (delta and pplus),
    second entry is the regular part.

spectrum-regular-x0.m:
    Expansion of the regular part around x=0.

spectrum-regular-y0.m:
    Expansion of the regular part around y=1-x=0.

decayrate.m:
    Analytic decay rate.

to_goncharov.m:
    Replacement rules to express iterated integrals in terms of Goncharov polylogarithms
    which can e.g. be evaluated in ginac.
    
constants.m:
    numeric evaluation of the constants c1, c2, c3
    
Symbols:

Color factor:
nc = Number of colors
CA = nc
CF = (nc^2-1)/2 nc
TF = 1/2
NH = number of flavors with mass mb
NL = number of massless quark flavors

Kinematics:
y = 1 - x
lmm1 = Log[mu^2/mb^2]
mb = bottom mass
mu = renormalization scale

Iterated integrals:
H[...,w1,y] = Integrate[ H[...,z] * f[w1][z] , {z,0,1} ], with the exception: H[0,...,0,y] = 1/n! * Log[y]^n, for n 0s.
f[-1][z] = 1/(1+z)
f[0][z] = 1/z
f[1][z] = 1/(1-z)
f[2][z] = 1/(2-z)
f[a][z] = Sqrt[(4-z)*z]
f[b][z] = f[a][z]/(1-z)

non standard constants: 
c1 = H[a,1]*H[a,2,1,1] - H[a,a,2,1,1]
c2 = H[a,1]*H[a,2,0,1] - H[a,a,2,0,1]
c3 = H[a,1]*H[a,2,1,0,1] - H[a,a,2,1,0,1]
