(* ::Package:: *)

(* contains the right-hand side of equations D2 to D24 (F[...]/NI) *)


(* the integrals which show up twice are given once with factors of (1-z) explicit, once with factors of z explicit *)


(* c*eps^n*DiracDelta[z] denotes that only the value at z=0 has been computed at this order (may be needed due to expansion of z^(-1-eps)), but not the full z dependence *)


(* see also integrated_splitting_functions_fragmenting_jet_in_mi.m *)


{
	YC[1, 1] -> ((1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2)/((1 - 2*eps)^2*z^eps*Gamma[1 - 2*eps]), 
	YC[1, 2] -> -(((1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2)/(z^eps*Gamma[2 - 2*eps])),
	YC[1, 3] -> -((eps*(1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2)/(z^eps*Gamma[2 - 2*eps])),
	YC[s[1, 2]^(-1), 0] -> -(((1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2*Hypergeometric2F1[1, 1 - eps, 2 - 2*eps, 1 - z])/(eps*z^eps*Gamma[2 - 2*eps])),
	YC[s[1, 2]^(-1), 1] -> ((1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2*Hypergeometric2F1[1, 1 - eps, 2 - 2*eps, 1 - z])/(eps*z^eps*Gamma[1 - 2*eps]),
	YC[s[1, 2]^(-1), 2] -> ((1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2*Hypergeometric2F1[1, 1 - eps, 2 - 2*eps, 1 - z])/(z^eps*Gamma[1 - 2*eps]),
	YC[s[1, 2]^(-1), 3] -> ((1 + 2*eps)*(1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2*Hypergeometric2F1[1, 1 - eps, 2 - 2*eps, 1 - z])/(3*z^eps*Gamma[1 - 2*eps]),
	YC[s[1, 2, 4]^(-1), 4] -> ((1 + 4*eps)*(3 - 9*eps - 8*eps^2 + 8*eps^3)*Gamma[1 - eps]^2*(((1 - z)^(-1 - 2*eps)*(1 + z))/z^eps - 2*(1 - z)^(-1 - 2*eps)*z^(1 - eps)*Hypergeometric2F1[1, -eps, -2*eps, 1 - z]))/(12*(1 - 2*eps)*(3 - 2*eps)*eps*Gamma[1 - 2*eps]),
	YC[s[1, 2]/s[1, 2, 4], 2] -> ((1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2)/(2*(1 - 2*eps)^2*z^eps*Gamma[1 - 2*eps]),
	YC[s[1, 2]/s[1, 2, 4], 3] -> -((2 - 7*eps + 4*eps^2)*(1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2)/(2*(1 - 2*eps)^2*(3 - 2*eps)*z^eps*Gamma[1 - 2*eps]),
	YC[s[1, 2]/s[1, 2, 4], 4] -> -((1 + eps - 12*eps^2 + 8*eps^3)*(1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2)/(4*(1 - 2*eps)^2*(3 - 2*eps)*z^eps*Gamma[1 - 2*eps]),
	YC[s[1, 3]/s[1, 2, 4], 2] -> (Gamma[1 - eps]^2*(-(((1 - z)^(-1 - 2*eps)*((1 + z)^2 - eps*(1 + 6*z + z^2)))/((1 - 2*eps)*z^eps)) + 2*(1 - z)^(-1 - 2*eps)*z^(1 - eps)*(1 + z)*Hypergeometric2F1[1, -eps, -2*eps, 1 - z]))/(2*(1 - 2*eps)*eps*Gamma[1 - 2*eps]),
	YC[s[1, 3]/s[1, 2, 4], 3] -> ((1 - z)^(-1 - 2*eps)*(-2*(1 + z)^2 + 3*eps*(3 + z)*(1 + 3*z) + eps^2*(-11 - 58*z - 11*z^2) + 4*eps^3*(1 + 6*z + z^2))*Gamma[1 - eps]^2)/(2*(1 - 2*eps)^2*eps*(-3 + 2*eps)*z^eps*Gamma[1 - 2*eps]) + (2*(1 - 4*eps + 2*eps^2)*(1 - z)^(-1 - 2*eps)*z^(1 - eps)*(1 + z)*Gamma[1 - eps]^2*Hypergeometric2F1[1, -eps, -2*eps, 1 - z])/((1 - 2*eps)*eps*(-3 + 2*eps)*Gamma[1 - 2*eps]),
	YC[s[1, 3]/s[1, 2, 4], 4] -> ((1 - z)^(-1 - 2*eps)*(4*eps*z - (1 + z)^2 - 20*eps^3*(1 + 6*z + z^2) + 8*eps^4*(1 + 6*z + z^2) + eps^2*(13 + 46*z + 13*z^2))*Gamma[1 - eps]^2)/(4*(1 - 2*eps)^2*eps*(-3 + 2*eps)*z^eps*Gamma[1 - 2*eps]) + ((1 + eps - 16*eps^2 + 8*eps^3)*(1 - z)^(-1 - 2*eps)*z^(1 - eps)*(1 + z)*Gamma[1 - eps]^2*Hypergeometric2F1[1, -eps, -2*eps, 1 - z])/(2*(1 - 2*eps)*eps*(-3 + 2*eps)*Gamma[1 - 2*eps]),
	YC[1/(s[1, 3]*s[1, 2, 4]), 0] -> (-2*Gamma[1 - eps]*Gamma[1 + eps])/(eps^2*z^(2*eps)*(1 + z)) + (2*(1 - z)^(1 - 2*eps)*Gamma[1 - eps]^2*Hypergeometric2F1[1, 1 - eps, 1 + eps, z])/(eps^2*z^eps*(1 + z)*Gamma[1 - 2*eps]),
	YC[1/(s[2, 3]*s[2, 4]*s[1, 2, 4]), 0] -> (((1 - z)*z)^(-1 - 2*eps)*Gamma[1 - eps]^2*Hypergeometric2F1[-2*eps, -eps, 1 - 2*eps, 1 - z])/(eps^2*Gamma[1 - 2*eps]),
	YC[1/(s[1, 2]*s[3, 4]*s[2, 3, 4]), 0] -> ((1 - z)^(-1 - 2*eps)*Gamma[1 - eps]^2)/(eps^2*z^eps*Gamma[1 - 2*eps]) - (Gamma[1 - eps]^2*Hypergeometric2F1[1, 1 - eps, 2 - 2*eps, 1 - z])/(eps*(1 - z)^(2*eps)*z^eps*Gamma[2 - 2*eps]),
	YC[1/(s[1, 2]*s[3, 4]*s[1, 3, 4]), 0] -> -(((1 - 3*z)*z^(-2 - eps)*Gamma[1 - eps]^2)/(eps^2*(1 - z)^(2*eps)*(1 + z)*Gamma[1 - 2*eps])) + ((1 - z)*z^(-1 - 2*eps)*Gamma[1 - eps]*Gamma[1 + eps])/(eps^2*(1 + z)) + ((1 - z)^(2 - 2*eps)*z^(-2 - eps)*Gamma[1 - eps]^2*Hypergeometric2F1[1, -eps, eps, z])/(eps^2*(1 + z)*Gamma[1 - 2*eps]),
	YC[1/(s[1, 2]*s[2, 4]*s[2, 3, 4]), 0] -> ((1 - z)^(-1 - 2*eps)*Gamma[1 - eps]^2*Hypergeometric2F1[1, 1 - eps, 1 - 2*eps, 1 - z])/(eps^2*z^eps*Gamma[1 - 2*eps]),
	YC[1/(s[1, 2]*s[1, 3]*s[2, 4]), -1] -> (2*z^(-1 - eps)*Gamma[1 - eps]^2)/(eps^2*(1 - z)^(2*eps)*Gamma[1 - 2*eps]) + (z^(-1 - 2*eps)*Gamma[1 - eps]^3*Gamma[1 + eps]^3)/(eps^3*Gamma[1 - 2*eps]*Gamma[2*eps]) - (2*z^(-1 - eps)*Gamma[1 - eps]^2*HypergeometricPFQ[{eps, eps, 2*eps}, {1 + eps, 1 + eps}, z])/(eps^2*Gamma[1 - 2*eps]) + (2*z^(-1 - 2*eps)*Gamma[1 - eps]*Gamma[1 + eps]*Log[z])/eps,
	YC[1/(s[1, 2]*s[2, 3]*s[1, 2, 4]), -1] -> (1/(eps^2*z) + Pi^2/(2*z) - (eps^2*Pi^4*DiracDelta[-1 + z])/40 - (2*HPL[{0}, z])/(eps*z) + (4*HPL[{0, 0}, z])/z + (4*HPL[{1, 0}, z])/z + eps*(-((Pi^2*HPL[{0}, z])/z) - (2*Pi^2*HPL[{1}, z])/z - (8*HPL[{2, 0}, z])/z - (8*HPL[{0, 0, 0}, z])/z - (12*HPL[{1, 0, 0}, z])/z - (12*HPL[{1, 1, 0}, z])/z + (6*Zeta[3])/z))/(1 - z)^(2*eps),
	YC[1/(s[1, 2]*s[2, 3]*s[1, 2, 4]), -1] -> z^(-1 - 2*eps)*(eps^(-2) + Pi^2/2 + (83*eps^2*Pi^4*DiracDelta[z])/360 + (2*HPL[{1}, z])/eps + 4*HPL[{1, 0}, z] + 4*HPL[{1, 1}, z] + eps*(-(Pi^2*HPL[{1}, z]) + 8*HPL[{1, 2}, z] + 4*HPL[{1, 0, 0}, z] + 4*HPL[{1, 1, 0}, z] + 8*HPL[{1, 1, 1}, z] + 6*Zeta[3])),
	YC[1/(s[1, 2]*s[2, 3]*s[3, 4]), -1] -> (1 - z)^(-1 - 2*eps)*(3/eps^2 - (5*Pi^2)/6 - (131*eps^2*Pi^4*DiracDelta[-1 + z])/360 - (2*HPL[{0}, z])/eps + eps*(Pi^2*HPL[{0}, z] + 4*HPL[{2, 0}, z] + 4*HPL[{0, 0, 0}, z] - 8*Zeta[3])),
	YC[1/(s[1, 2]*s[2, 3]*s[3, 4]), -1] -> (-(1/(eps^2*(1 - z))) - Pi^2/(6*(1 - z)) - (7*eps^2*Pi^4*DiracDelta[z])/360 - (2*HPL[{1}, z])/(eps*(1 - z)) - (4*HPL[{2}, z])/(1 - z) - (4*HPL[{1, 1}, z])/(1 - z) + eps*(-(Pi^2*HPL[{1}, z])/(3*(1 - z)) - (8*HPL[{3}, z])/(1 - z) - (8*HPL[{1, 2}, z])/(1 - z) - (8*HPL[{2, 1}, z])/(1 - z) - (8*HPL[{1, 1, 1}, z])/(1 - z)))/z^(2*eps) + (4/(eps^2*(1 - z)) - (2*Pi^2)/(3*(1 - z)) - (eps^2*Pi^4*DiracDelta[z])/10 + (8*HPL[{1}, z])/(eps*(1 - z)) + (4*HPL[{2}, z])/(1 - z) + (16*HPL[{1, 1}, z])/(1 - z) + eps*((-4*Pi^2*HPL[{1}, z])/(3*(1 - z)) + (8*HPL[{1, 2}, z])/(1 - z) + (8*HPL[{2, 1}, z])/(1 - z) + (32*HPL[{1, 1, 1}, z])/(1 - z) - (8*Zeta[3])/(1 - z)))/z^eps,
	YC[1/(s[1, 2]*s[1, 3]*s[1, 2, 4]), -1] -> (1 - z)^(1 - 2*eps)*(-Pi^2/(3*(1 - z)*z) + (2*HPL[{0}, z])/(eps*(1 - z)*z) + (4*HPL[{-1, 0}, z])/((1 - z)*z) - (8*HPL[{0, 0}, z])/((1 - z)*z) - (4*HPL[{1, 0}, z])/((1 - z)*z) + (eps^3*DiracDelta[-1 + z]*(-1920 + 80*Pi^2 + 3*Pi^4 + 480*Zeta[3]))/60 + eps*((-4*Pi^2*HPL[{-1}, z])/(3*(1 - z)*z) + (Pi^2*HPL[{0}, z])/((1 - z)*z) + (2*Pi^2*HPL[{1}, z])/(3*(1 - z)*z) - (8*HPL[{-2, 0}, z])/((1 - z)*z) + (12*HPL[{2, 0}, z])/((1 - z)*z) - (12*HPL[{-1, 0, 0}, z])/((1 - z)*z) - (8*HPL[{-1, 1, 0}, z])/((1 - z)*z) + (24*HPL[{0, 0, 0}, z])/((1 - z)*z) - (8*HPL[{1, -1, 0}, z])/((1 - z)*z) + (16*HPL[{1, 0, 0}, z])/((1 - z)*z) + (8*HPL[{1, 1, 0}, z])/((1 - z)*z) + (2*Zeta[3])/((1 - z)*z)) + eps^2*((-7*Pi^4)/(90*(1 - z)*z) + (8*Pi^2*HPL[{-2}, z])/(3*(1 - z)*z) - (8*Pi^2*HPL[{2}, z])/(3*(1 - z)*z) + (16*HPL[{-3, 0}, z])/((1 - z)*z) + (2*Pi^2*HPL[{-1, 0}, z])/((1 - z)*z) + (8*Pi^2*HPL[{-1, 1}, z])/(3*(1 - z)*z) - (8*Pi^2*HPL[{0, 0}, z])/(3*(1 - z)*z) + (8*Pi^2*HPL[{1, -1}, z])/(3*(1 - z)*z) - (2*Pi^2*HPL[{1, 0}, z])/((1 - z)*z) - (4*Pi^2*HPL[{1, 1}, z])/(3*(1 - z)*z) - (32*HPL[{3, 0}, z])/((1 - z)*z) + (24*HPL[{-2, 0, 0}, z])/((1 - z)*z) + (16*HPL[{-2, 1, 0}, z])/((1 - z)*z) + (16*HPL[{-1, 2, 0}, z])/((1 - z)*z) + (16*HPL[{1, -2, 0}, z])/((1 - z)*z) - (24*HPL[{1, 2, 0}, z])/((1 - z)*z) + (16*HPL[{2, -1, 0}, z])/((1 - z)*z) - (44*HPL[{2, 0, 0}, z])/((1 - z)*z) - (24*HPL[{2, 1, 0}, z])/((1 - z)*z) + (28*HPL[{-1, 0, 0, 0}, z])/((1 - z)*z) + (24*HPL[{-1, 1, 0, 0}, z])/((1 - z)*z) + (16*HPL[{-1, 1, 1, 0}, z])/((1 - z)*z) - (64*HPL[{0, 0, 0, 0}, z])/((1 - z)*z) + (24*HPL[{1, -1, 0, 0}, z])/((1 - z)*z) + (16*HPL[{1, -1, 1, 0}, z])/((1 - z)*z) - (48*HPL[{1, 0, 0, 0}, z])/((1 - z)*z) + (16*HPL[{1, 1, -1, 0}, z])/((1 - z)*z) - (32*HPL[{1, 1, 0, 0}, z])/((1 - z)*z) - (16*HPL[{1, 1, 1, 0}, z])/((1 - z)*z) - (8*HPL[{-1}, z]*Zeta[3])/((1 - z)*z) - (4*HPL[{0}, z]*Zeta[3])/((1 - z)*z) - (4*HPL[{1}, z]*Zeta[3])/((1 - z)*z))),
	YC[1/(s[1, 2]*s[1, 3]*s[1, 2, 4]), -1] -> 2*z^(-1 - 2*eps)*Gamma[1 - eps]*Gamma[eps]*HPL[{0}, z] + z^(-1 - 2*eps)*(-Pi^2/3 + 4*HPL[{2}, z] + 4*HPL[{-1, 0}, z] + eps^3*OrderGuard["eps"] + eps*((-4*Pi^2*HPL[{-1}, z])/3 + 8*HPL[{-1, 2}, z] + 4*HPL[{2, 0}, z] + 8*HPL[{2, 1}, z] + 4*HPL[{-1, 0, 0}, z] + 2*Zeta[3]) + eps^2*((-7*Pi^4)/90 - (2*Pi^2*HPL[{2}, z])/3 - (2*Pi^2*HPL[{-1, 0}, z])/3 + 8*HPL[{-1, 3}, z] + 8*HPL[{2, 2}, z] + 8*HPL[{-1, 2, 0}, z] + 16*HPL[{-1, 2, 1}, z] + 4*HPL[{2, 0, 0}, z] + 8*HPL[{2, 1, 0}, z] + 16*HPL[{2, 1, 1}, z] + 4*HPL[{-1, 0, 0, 0}, z] - 8*HPL[{-1}, z]*Zeta[3]))
}