(* ::Package:: *)

(* jth expansion term in the hard, collinear-1 and collinear-2 regions*)

Fjh[n1_,n2_,n3_,j_] := m1Pow[n1+n2+n3] Pochhammer[n3,j]/j!*((-1)^j m2^j)/Q2^(n1+n2+n3+j-2+eps)*(Gamma[n1+n2+n3+j-2+eps]Gamma[2-n1-n3-j-eps]Gamma[2-n2-n3-j-eps])/(Gamma[n1]Gamma[n2]Gamma[4-2eps-n1-n2-n3-j])/.{m1Pow[n_] /; IntegerQ[n]:>(-1)^n};
Fjc1[n1_,n2_,n3_,j_] := m1Pow[n1+n2+n3] Pochhammer[n2,j]/j!*((-1)^j m2^(2-eps-n1-n3+j))/Q2^(n2+j)*(Gamma[n1-n2-j]Gamma[2-n1+j-eps]Gamma[n1+n3-j-2+eps])/(Gamma[n1]Gamma[n3]Gamma[2-eps-n2-j])/.{m1Pow[n_] /; IntegerQ[n]:>(-1)^n};
Fjc2[n1_,n2_,n3_,j_] := Fjc1[n2,n1,n3,j];


(* Hard region *)
Series[Q2^(1+eps)*Exp[eps*EulerGamma]*Fjh[1,1,1,0],{eps,0,0}]
Series[Q2^(2+eps)/m2*Exp[eps*EulerGamma]*Fjh[1,1,1,1],{eps,0,0}]
Series[Q2^(3+eps)/m2^2*Exp[eps*EulerGamma]*Fjh[1,1,1,2],{eps,0,0}]


(* 1-collinear region *)
Series[Q2^(1-del)*m2^(eps+del)*Exp[eps*EulerGamma]*Fjc1[1+del,1-del,1,0],{del,0,0},{eps,0,0}]
Series[Q2^(2-del)*m2^(-1+eps+del)*Exp[eps*EulerGamma]*Fjc1[1+del,1-del,1,1],{del,0,0},{eps,0,0}]
Series[Q2^(3-del)*m2^(-2+eps+del)*Exp[eps*EulerGamma]*Fjc1[1+del,1-del,1,2],{del,0,0},{eps,0,0}]


(* 2-collinear region *)
Series[Q2^(1+del)*m2^(eps-del)*Exp[eps*EulerGamma]*Fjc2[1+del,1-del,1,0],{del,0,0},{eps,0,0}]
Series[Q2^(2+del)*m2^(-1+eps-del)*Exp[eps*EulerGamma]*Fjc2[1+del,1-del,1,1],{del,0,0},{eps,0,0}]
Series[Q2^(3+del)*m2^(-2+eps-del)*Exp[eps*EulerGamma]*Fjc2[1+del,1-del,1,2],{del,0,0},{eps,0,0}]


(*Sum over all regions*)
res0 = Series[Q2*Exp[eps*EulerGamma]*(Fjh[1+del,1-del,1,0]+Fjc1[1+del,1-del,1,0]+Fjc2[1+del,1-del,1,0]),{del,0,0},{eps,0,0}]
res1 = Series[Q2^2/m2*Exp[eps*EulerGamma]*(Fjh[1+del,1-del,1,1]+Fjc1[1+del,1-del,1,1]+Fjc2[1+del,1-del,1,1]),{del,0,0},{eps,0,0}]
res2 = Series[Q2^3/m2^2*Exp[eps*EulerGamma]*(Fjh[1+del,1-del,1,2]+Fjc1[1+del,1-del,1,2]+Fjc2[1+del,1-del,1,2]),{del,0,0},{eps,0,0}]


(* Full result with z = m2/Q2 *)
Ffull = -1/Q2*(1/2 Log[z]^2-Log[z]*Log[1-z] - PolyLog[2,z] + \[Pi]^2/3);
Series[Ffull,{z,0,2}]


(* Check *)
Series[Ffull - (res0+res1*z+res2*z^2 /. {m2->z,Q2->1})/Q2,{z,0,2}]