**************************************************************** * * 4F3 with integer parameters * * Any four functions of FI43,FI43A,FI43B,FI43C,FI43D,FI43E,FI43F, * * are basis for eduction of 4F3[I1+a1*ep,I2+a2*ep,I3+a3*ep, I4+a4*ep; I5+b1*ep,I6+b2*ep, I7*ep; z] **************************************************************** * * FI43 = Hypergeometric3F2[a1*ep, a2*ep, a3*ep, a4*ep; 1+c1*ep, 1+c2*ep, 1+c3*ep;z] * * FI43A = Hypergeometric4F3[1+a1*ep, 1+a2*ep, 1+a3*ep, 1+a4*ep; 2+c1*ep, 2+c2*ep, 2+c3*ep;z] * * FI43B = Hypergeometric3F2[1+a1*ep,1+a2*ep,1+a3*ep,2+d1*ep; 2+c1*ep, 2+c2*ep, 2+c3*ep;z] * * FI43C = Hypergeometric3F2[1+a1*ep,1+a2*ep,2+d1*ep,2+d2*ep; 2+c1*ep, 2+c2*ep, 2+c3*ep;z] * * FI43D = Hypergeometric4F3[1+a1*ep, 1+a2*ep, 1+a3*ep, 1+a4*ep; 2+c1*ep, 2+c2*ep, 1+e1*ep;z] * * FI43E = Hypergeometric3F2[1+a1*ep,1+a2*ep,1+a3*ep,1+a4*ep; 2+c1*ep, 1+e1*ep, 1+e2*ep;z] * * FI43F = Hypergeometric3F2[1+a1*ep,1+a2*ep,1+c3*ep,2+d1*ep; 2+c1*ep, 2+c2*ep, 1+e1*ep;z] * * "a1","a2","a3", "a4", "d1","d2", "c1", "c2", "c3" are the epsilon dependent part of parameters; * "z" is argument of hypergeometric function * "ep" is difference between dimention of space-time and integer values of parameters (small parameter) * * [1+d1*ep] = 1+d1*ep; * [1+d2*ep] = 1+d2*ep; * [1+c1*ep] = 1*c1*ep; * [1+c2*ep] = 1*c2*ep; * [1+c3*ep] = 1*c3*ep; * "zt" is Zeta-function, "ln" is logarithm * "Li" and "S" are classical and Nielsen polylgarithms. * * * **************************************************************************************** s a1,a2,a3,a4,b1,c1,c2,c3,d1,d2,e1,e2,ep,z,[1+d1*ep],[1+d2*ep],[1+c1*ep],[1+c2*ep],[1+c3*ep]; c Li,S,zt,ln; c FI43, FI43A, FI43B, FI43C, FI43D, FI43E, FI43F, FI54A; * Example of calling: g TEST1 = FI43A(1,2,3,4,5,4,3,z,ep); g TEST2 = FI43B(1,2,3,4,5,4,3,z,ep); g TEST3 = FI43C(1,2,3,4,5,4,3,z,ep); g TEST4 = FI43D(1,2,3,4,5,4,3,z,ep); g TEST5 = FI43E(1,2,3,4,5,4,3,z,ep); g TEST6 = FI43F(1,2,3,4,5,4,3,z,ep); g TEST7 = FI43(1,2,3,4,5,4,3,z,ep); **************************************************************************************** * FI43 = Hypergeometric4F3[a1*ep,a2*ep,a3*ep,a4*ep; 1+c1*ep, 1+c2*ep,1+c3*ep;z] **************************************************************************************** id FI43(a1?,a2?,a3?,a4?,c1?,c2?,c3?,z?,ep?) = 1 + a1*a2*a3*a4*ep^4/[1+c1*ep]/[1+c2*ep]/[1+c3*ep]*FI54A(0,a1,a2,a3,a4,0,c1,c2,c3,z,ep); .sort **************************************************************************************** * FI43A = Hypergeometric4F3[1+a1*ep,1+a2*ep,1+a3*ep,1+a4*ep; 2+c1*ep, 2+c2*ep,2+c3*ep;z] **************************************************************************************** id FI43A(a1?,a2?,a3?,a4?,c1?,c2?,c3?,z?,ep?) = 1/z*[1+c1*ep]*[1+c2*ep]*[1+c3*ep]*( + Li(3,z) + ep * ( - S(2,2,z)*c3 - S(2,2,z)*c2 - S(2,2,z)*c1 + S(2,2,z)*a4 + S(2,2,z)*a3 + S(2,2,z)*a2 + S(2,2,z)*a1 - Li(4,z)*c3 - Li(4,z)*c2 - Li(4,z)*c1 ) + ep^2*FI43A(a1,a2,a3,a4,c1,c2,c3,z,ep^2) ); .sort **************************************************************************************** * FI43B = Hypergeometric4F3[1+a1*ep,1+a2*ep,1+a3*ep,2+d1*ep; 2+c1*ep, 2+c2*ep, 2+c3*ep;z] **************************************************************************************** id FI43B(a1?,a2?,a3?,d1?,c1?,c2?,c3?,z?,ep?) = 1/z*[1+c1*ep]*[1+c2*ep]*[1+c3*ep]/[1+d1*ep]*( + Li(2,z) + ep * ( S(1,2,z)*d1 - S(1,2,z)*c3 - S(1,2,z)*c2 - S(1,2,z)*c1 + S(1,2, z)*a3 + S(1,2,z)*a2 + S(1,2,z)*a1 + Li(3,z)*d1 - Li(3,z)*c3 - Li(3,z) *c2 - Li(3,z)*c1 ) + ep^2 * ( S(1,3,z)*d1^2 - 2*S(1,3,z)*c3*d1 + S(1,3,z)*c3^2 - 2*S(1,3,z )*c2*d1 + 2*S(1,3,z)*c2*c3 + S(1,3,z)*c2^2 - 2*S(1,3,z)*c1*d1 + 2*S(1 ,3,z)*c1*c3 + 2*S(1,3,z)*c1*c2 + S(1,3,z)*c1^2 + 2*S(1,3,z)*a3*d1 - 2 *S(1,3,z)*a3*c3 - 2*S(1,3,z)*a3*c2 - 2*S(1,3,z)*a3*c1 + S(1,3,z)*a3^2 + 2*S(1,3,z)*a2*d1 - 2*S(1,3,z)*a2*c3 - 2*S(1,3,z)*a2*c2 - 2*S(1,3,z )*a2*c1 + 2*S(1,3,z)*a2*a3 + S(1,3,z)*a2^2 + 2*S(1,3,z)*a1*d1 - 2*S(1 ,3,z)*a1*c3 - 2*S(1,3,z)*a1*c2 - 2*S(1,3,z)*a1*c1 + 2*S(1,3,z)*a1*a3 + 2*S(1,3,z)*a1*a2 + S(1,3,z)*a1^2 + S(2,2,z)*d1^2 - S(2,2,z)*c3^2 - S(2,2,z)*c2^2 - S(2,2,z)*c1^2 - S(2,2,z)*a3*d1 + S(2,2,z)*a3*c3 + S(2,2,z)*a3*c2 + S(2,2,z)*a3*c1 - S(2,2,z)*a2*d1 + S(2,2,z)*a2*c3 + S(2,2,z)*a2*c2 + S(2,2,z)*a2*c1 - 2*S(2,2,z)*a2*a3 - S(2,2,z)*a1*d1 + S(2,2,z)*a1*c3 + S(2,2,z)*a1*c2 + S(2,2,z)*a1*c1 - 2*S(2,2,z)*a1* a3 - 2*S(2,2,z)*a1*a2 - 1/2*Li(2,z)^2*c3*d1 + 1/2*Li(2,z)^2*c3^2 - 1/ 2*Li(2,z)^2*c2*d1 + 1/2*Li(2,z)^2*c2*c3 + 1/2*Li(2,z)^2*c2^2 - 1/2* Li(2,z)^2*c1*d1 + 1/2*Li(2,z)^2*c1*c3 + 1/2*Li(2,z)^2*c1*c2 + 1/2*Li( 2,z)^2*c1^2 + 1/2*Li(2,z)^2*a3*d1 - 1/2*Li(2,z)^2*a3*c3 - 1/2*Li(2,z) ^2*a3*c2 - 1/2*Li(2,z)^2*a3*c1 + 1/2*Li(2,z)^2*a2*d1 - 1/2*Li(2,z)^2* a2*c3 - 1/2*Li(2,z)^2*a2*c2 - 1/2*Li(2,z)^2*a2*c1 + 1/2*Li(2,z)^2*a2* a3 + 1/2*Li(2,z)^2*a1*d1 - 1/2*Li(2,z)^2*a1*c3 - 1/2*Li(2,z)^2*a1*c2 - 1/2*Li(2,z)^2*a1*c1 + 1/2*Li(2,z)^2*a1*a3 + 1/2*Li(2,z)^2*a1*a2 - Li(4,z)*c3*d1 + Li(4,z)*c3^2 - Li(4,z)*c2*d1 + Li(4,z)*c2*c3 + Li(4,z )*c2^2 - Li(4,z)*c1*d1 + Li(4,z)*c1*c3 + Li(4,z)*c1*c2 + Li(4,z)*c1^2 ) + ep^3*FI43B(a1,a2,a3,d1,c1,c2,c3,z,ep^3) ); .sort **************************************************************************************** * FI43C = Hypergeometric4F3[1+a1*ep,1+a2*ep,2+d1*ep,2+d2*ep; 2+c1*ep, 2+c2*ep, 2+c3*ep;z] **************************************************************************************** id FI43C(a1?,a2?,d1?,d2?,c1?,c2?,c3?,z?,ep?) = 1/z*[1+c1*ep]*[1+c2*ep]*[1+c3*ep]/[1+d1*ep]/[1+d2*ep]*( - ln(1 - z) + ep * ( 1/2*ln(1 - z)^2*d2 + 1/2*ln(1 - z)^2*d1 - 1/2*ln(1 - z)^2*c3 - 1/2*ln(1 - z)^2*c2 - 1/2*ln(1 - z)^2*c1 + 1/2*ln(1 - z)^2*a2 + 1/2 *ln(1 - z)^2*a1 + Li(2,z)*d2 + Li(2,z)*d1 - Li(2,z)*c3 - Li(2,z)*c2 - Li(2,z)*c1 ) + ep^2 * ( S(1,2,z)*d2^2 + S(1,2,z)*d1^2 - S(1,2,z)*c3^2 - S(1,2,z)* c2^2 - S(1,2,z)*c1^2 - S(1,2,z)*a2*d2 - S(1,2,z)*a2*d1 + S(1,2,z)*a2* c3 + S(1,2,z)*a2*c2 + S(1,2,z)*a2*c1 - S(1,2,z)*a1*d2 - S(1,2,z)*a1* d1 + S(1,2,z)*a1*c3 + S(1,2,z)*a1*c2 + S(1,2,z)*a1*c1 - 2*S(1,2,z)*a1 *a2 - 1/6*ln(1 - z)^3*d2^2 - 1/3*ln(1 - z)^3*d1*d2 - 1/6*ln(1 - z)^3* d1^2 + 1/3*ln(1 - z)^3*c3*d2 + 1/3*ln(1 - z)^3*c3*d1 - 1/6*ln(1 - z)^ 3*c3^2 + 1/3*ln(1 - z)^3*c2*d2 + 1/3*ln(1 - z)^3*c2*d1 - 1/3*ln(1 - z )^3*c2*c3 - 1/6*ln(1 - z)^3*c2^2 + 1/3*ln(1 - z)^3*c1*d2 + 1/3*ln(1 - z)^3*c1*d1 - 1/3*ln(1 - z)^3*c1*c3 - 1/3*ln(1 - z)^3*c1*c2 - 1/6* ln(1 - z)^3*c1^2 - 1/3*ln(1 - z)^3*a2*d2 - 1/3*ln(1 - z)^3*a2*d1 + 1/ 3*ln(1 - z)^3*a2*c3 + 1/3*ln(1 - z)^3*a2*c2 + 1/3*ln(1 - z)^3*a2*c1 - 1/6*ln(1 - z)^3*a2^2 - 1/3*ln(1 - z)^3*a1*d2 - 1/3*ln(1 - z)^3*a1* d1 + 1/3*ln(1 - z)^3*a1*c3 + 1/3*ln(1 - z)^3*a1*c2 + 1/3*ln(1 - z)^3* a1*c1 - 1/3*ln(1 - z)^3*a1*a2 - 1/6*ln(1 - z)^3*a1^2 - ln(1 - z)*Li(2 ,z)*d1*d2 + ln(1 - z)*Li(2,z)*c3*d2 + ln(1 - z)*Li(2,z)*c3*d1 - ln(1 - z)*Li(2,z)*c3^2 + ln(1 - z)*Li(2,z)*c2*d2 + ln(1 - z)*Li(2,z)*c2* d1 - ln(1 - z)*Li(2,z)*c2*c3 - ln(1 - z)*Li(2,z)*c2^2 + ln(1 - z)*Li( 2,z)*c1*d2 + ln(1 - z)*Li(2,z)*c1*d1 - ln(1 - z)*Li(2,z)*c1*c3 - ln(1 - z)*Li(2,z)*c1*c2 - ln(1 - z)*Li(2,z)*c1^2 - ln(1 - z)*Li(2,z)*a2* d2 - ln(1 - z)*Li(2,z)*a2*d1 + ln(1 - z)*Li(2,z)*a2*c3 + ln(1 - z)* Li(2,z)*a2*c2 + ln(1 - z)*Li(2,z)*a2*c1 - ln(1 - z)*Li(2,z)*a1*d2 - ln(1 - z)*Li(2,z)*a1*d1 + ln(1 - z)*Li(2,z)*a1*c3 + ln(1 - z)*Li(2,z) *a1*c2 + ln(1 - z)*Li(2,z)*a1*c1 - ln(1 - z)*Li(2,z)*a1*a2 + Li(3,z)* d1*d2 - Li(3,z)*c3*d2 - Li(3,z)*c3*d1 + Li(3,z)*c3^2 - Li(3,z)*c2*d2 - Li(3,z)*c2*d1 + Li(3,z)*c2*c3 + Li(3,z)*c2^2 - Li(3,z)*c1*d2 - Li( 3,z)*c1*d1 + Li(3,z)*c1*c3 + Li(3,z)*c1*c2 + Li(3,z)*c1^2 ) + ep^3 * ( S(1,2,z)*ln(1 - z)*d1*d2^2 + S(1,2,z)*ln(1 - z)*d1^2*d2 - S( 1,2,z)*ln(1 - z)*c3*d2^2 - 3*S(1,2,z)*ln(1 - z)*c3*d1*d2 - S(1,2,z)* ln(1 - z)*c3*d1^2 + 2*S(1,2,z)*ln(1 - z)*c3^2*d2 + 2*S(1,2,z)*ln(1 - z)*c3^2*d1 - S(1,2,z)*ln(1 - z)*c3^3 - S(1,2,z)*ln(1 - z)*c2*d2^2 - 3 *S(1,2,z)*ln(1 - z)*c2*d1*d2 - S(1,2,z)*ln(1 - z)*c2*d1^2 + 3*S(1,2,z )*ln(1 - z)*c2*c3*d2 + 3*S(1,2,z)*ln(1 - z)*c2*c3*d1 - 2*S(1,2,z)*ln( 1 - z)*c2*c3^2 + 2*S(1,2,z)*ln(1 - z)*c2^2*d2 + 2*S(1,2,z)*ln(1 - z)* c2^2*d1 - 2*S(1,2,z)*ln(1 - z)*c2^2*c3 - S(1,2,z)*ln(1 - z)*c2^3 - S( 1,2,z)*ln(1 - z)*c1*d2^2 - 3*S(1,2,z)*ln(1 - z)*c1*d1*d2 - S(1,2,z)* ln(1 - z)*c1*d1^2 + 3*S(1,2,z)*ln(1 - z)*c1*c3*d2 + 3*S(1,2,z)*ln(1 - z)*c1*c3*d1 - 2*S(1,2,z)*ln(1 - z)*c1*c3^2 + 3*S(1,2,z)*ln(1 - z)* c1*c2*d2 + 3*S(1,2,z)*ln(1 - z)*c1*c2*d1 - 3*S(1,2,z)*ln(1 - z)*c1*c2 *c3 - 2*S(1,2,z)*ln(1 - z)*c1*c2^2 + 2*S(1,2,z)*ln(1 - z)*c1^2*d2 + 2 *S(1,2,z)*ln(1 - z)*c1^2*d1 - 2*S(1,2,z)*ln(1 - z)*c1^2*c3 - 2*S(1,2, z)*ln(1 - z)*c1^2*c2 - S(1,2,z)*ln(1 - z)*c1^3 + S(1,2,z)*ln(1 - z)* a2*d2^2 + 3*S(1,2,z)*ln(1 - z)*a2*d1*d2 + S(1,2,z)*ln(1 - z)*a2*d1^2 - 3*S(1,2,z)*ln(1 - z)*a2*c3*d2 - 3*S(1,2,z)*ln(1 - z)*a2*c3*d1 + 2* S(1,2,z)*ln(1 - z)*a2*c3^2 - 3*S(1,2,z)*ln(1 - z)*a2*c2*d2 - 3*S(1,2, z)*ln(1 - z)*a2*c2*d1 + 3*S(1,2,z)*ln(1 - z)*a2*c2*c3 + 2*S(1,2,z)* ln(1 - z)*a2*c2^2 - 3*S(1,2,z)*ln(1 - z)*a2*c1*d2 - 3*S(1,2,z)*ln(1 - z)*a2*c1*d1 + 3*S(1,2,z)*ln(1 - z)*a2*c1*c3 + 3*S(1,2,z)*ln(1 - z) *a2*c1*c2 + 2*S(1,2,z)*ln(1 - z)*a2*c1^2 + S(1,2,z)*ln(1 - z)*a2^2*d2 + S(1,2,z)*ln(1 - z)*a2^2*d1 - S(1,2,z)*ln(1 - z)*a2^2*c3 - S(1,2,z) *ln(1 - z)*a2^2*c2 - S(1,2,z)*ln(1 - z)*a2^2*c1 + S(1,2,z)*ln(1 - z)* a1*d2^2 + 3*S(1,2,z)*ln(1 - z)*a1*d1*d2 + S(1,2,z)*ln(1 - z)*a1*d1^2 - 3*S(1,2,z)*ln(1 - z)*a1*c3*d2 - 3*S(1,2,z)*ln(1 - z)*a1*c3*d1 + 2* S(1,2,z)*ln(1 - z)*a1*c3^2 - 3*S(1,2,z)*ln(1 - z)*a1*c2*d2 - 3*S(1,2, z)*ln(1 - z)*a1*c2*d1 + 3*S(1,2,z)*ln(1 - z)*a1*c2*c3 + 2*S(1,2,z)* ln(1 - z)*a1*c2^2 - 3*S(1,2,z)*ln(1 - z)*a1*c1*d2 - 3*S(1,2,z)*ln(1 - z)*a1*c1*d1 + 3*S(1,2,z)*ln(1 - z)*a1*c1*c3 + 3*S(1,2,z)*ln(1 - z) *a1*c1*c2 + 2*S(1,2,z)*ln(1 - z)*a1*c1^2 + 3*S(1,2,z)*ln(1 - z)*a1*a2 *d2 + 3*S(1,2,z)*ln(1 - z)*a1*a2*d1 - 3*S(1,2,z)*ln(1 - z)*a1*a2*c3 - 3*S(1,2,z)*ln(1 - z)*a1*a2*c2 - 3*S(1,2,z)*ln(1 - z)*a1*a2*c1 + S( 1,2,z)*ln(1 - z)*a1*a2^2 + S(1,2,z)*ln(1 - z)*a1^2*d2 + S(1,2,z)*ln(1 - z)*a1^2*d1 - S(1,2,z)*ln(1 - z)*a1^2*c3 - S(1,2,z)*ln(1 - z)*a1^2* c2 - S(1,2,z)*ln(1 - z)*a1^2*c1 + S(1,2,z)*ln(1 - z)*a1^2*a2 + S(1,3, z)*d2^3 + 3*S(1,3,z)*d1*d2^2 + 3*S(1,3,z)*d1^2*d2 + S(1,3,z)*d1^3 - 3 *S(1,3,z)*c3*d2^2 - 6*S(1,3,z)*c3*d1*d2 - 3*S(1,3,z)*c3*d1^2 + 3*S(1, 3,z)*c3^2*d2 + 3*S(1,3,z)*c3^2*d1 - S(1,3,z)*c3^3 - 3*S(1,3,z)*c2* d2^2 - 6*S(1,3,z)*c2*d1*d2 - 3*S(1,3,z)*c2*d1^2 + 6*S(1,3,z)*c2*c3*d2 + 6*S(1,3,z)*c2*c3*d1 - 3*S(1,3,z)*c2*c3^2 + 3*S(1,3,z)*c2^2*d2 + 3* S(1,3,z)*c2^2*d1 - 3*S(1,3,z)*c2^2*c3 - S(1,3,z)*c2^3 - 3*S(1,3,z)*c1 *d2^2 - 6*S(1,3,z)*c1*d1*d2 - 3*S(1,3,z)*c1*d1^2 + 6*S(1,3,z)*c1*c3* d2 + 6*S(1,3,z)*c1*c3*d1 - 3*S(1,3,z)*c1*c3^2 + 6*S(1,3,z)*c1*c2*d2 + 6*S(1,3,z)*c1*c2*d1 - 6*S(1,3,z)*c1*c2*c3 - 3*S(1,3,z)*c1*c2^2 + 3 *S(1,3,z)*c1^2*d2 + 3*S(1,3,z)*c1^2*d1 - 3*S(1,3,z)*c1^2*c3 - 3*S(1,3 ,z)*c1^2*c2 - S(1,3,z)*c1^3 + 2*S(1,3,z)*a2*d2^2 + 4*S(1,3,z)*a2*d1* d2 + 2*S(1,3,z)*a2*d1^2 - 4*S(1,3,z)*a2*c3*d2 - 4*S(1,3,z)*a2*c3*d1 + 2*S(1,3,z)*a2*c3^2 - 4*S(1,3,z)*a2*c2*d2 - 4*S(1,3,z)*a2*c2*d1 + 4 *S(1,3,z)*a2*c2*c3 + 2*S(1,3,z)*a2*c2^2 - 4*S(1,3,z)*a2*c1*d2 - 4*S(1 ,3,z)*a2*c1*d1 + 4*S(1,3,z)*a2*c1*c3 + 4*S(1,3,z)*a2*c1*c2 + 2*S(1,3, z)*a2*c1^2 + S(1,3,z)*a2^2*d2 + S(1,3,z)*a2^2*d1 - S(1,3,z)*a2^2*c3 - S(1,3,z)*a2^2*c2 - S(1,3,z)*a2^2*c1 + 2*S(1,3,z)*a1*d2^2 + 4*S(1,3 ,z)*a1*d1*d2 + 2*S(1,3,z)*a1*d1^2 - 4*S(1,3,z)*a1*c3*d2 - 4*S(1,3,z)* a1*c3*d1 + 2*S(1,3,z)*a1*c3^2 - 4*S(1,3,z)*a1*c2*d2 - 4*S(1,3,z)*a1* c2*d1 + 4*S(1,3,z)*a1*c2*c3 + 2*S(1,3,z)*a1*c2^2 - 4*S(1,3,z)*a1*c1* d2 - 4*S(1,3,z)*a1*c1*d1 + 4*S(1,3,z)*a1*c1*c3 + 4*S(1,3,z)*a1*c1*c2 + 2*S(1,3,z)*a1*c1^2 + 2*S(1,3,z)*a1*a2*d2 + 2*S(1,3,z)*a1*a2*d1 - 2 *S(1,3,z)*a1*a2*c3 - 2*S(1,3,z)*a1*a2*c2 - 2*S(1,3,z)*a1*a2*c1 + S(1, 3,z)*a1^2*d2 + S(1,3,z)*a1^2*d1 - S(1,3,z)*a1^2*c3 - S(1,3,z)*a1^2*c2 - S(1,3,z)*a1^2*c1 - S(2,2,z)*d1*d2^2 - S(2,2,z)*d1^2*d2 + S(2,2,z)* c3*d2^2 + 3*S(2,2,z)*c3*d1*d2 + S(2,2,z)*c3*d1^2 - 2*S(2,2,z)*c3^2*d2 - 2*S(2,2,z)*c3^2*d1 + S(2,2,z)*c3^3 + S(2,2,z)*c2*d2^2 + 3*S(2,2,z) *c2*d1*d2 + S(2,2,z)*c2*d1^2 - 3*S(2,2,z)*c2*c3*d2 - 3*S(2,2,z)*c2*c3 *d1 + 2*S(2,2,z)*c2*c3^2 - 2*S(2,2,z)*c2^2*d2 - 2*S(2,2,z)*c2^2*d1 + 2*S(2,2,z)*c2^2*c3 + S(2,2,z)*c2^3 + S(2,2,z)*c1*d2^2 + 3*S(2,2,z)*c1 *d1*d2 + S(2,2,z)*c1*d1^2 - 3*S(2,2,z)*c1*c3*d2 - 3*S(2,2,z)*c1*c3*d1 + 2*S(2,2,z)*c1*c3^2 - 3*S(2,2,z)*c1*c2*d2 - 3*S(2,2,z)*c1*c2*d1 + 3 *S(2,2,z)*c1*c2*c3 + 2*S(2,2,z)*c1*c2^2 - 2*S(2,2,z)*c1^2*d2 - 2*S(2, 2,z)*c1^2*d1 + 2*S(2,2,z)*c1^2*c3 + 2*S(2,2,z)*c1^2*c2 + S(2,2,z)* c1^3 - 2*S(2,2,z)*a2*d2^2 - 3*S(2,2,z)*a2*d1*d2 - 2*S(2,2,z)*a2*d1^2 + 3*S(2,2,z)*a2*c3*d2 + 3*S(2,2,z)*a2*c3*d1 - S(2,2,z)*a2*c3^2 + 3* S(2,2,z)*a2*c2*d2 + 3*S(2,2,z)*a2*c2*d1 - 3*S(2,2,z)*a2*c2*c3 - S(2,2 ,z)*a2*c2^2 + 3*S(2,2,z)*a2*c1*d2 + 3*S(2,2,z)*a2*c1*d1 - 3*S(2,2,z)* a2*c1*c3 - 3*S(2,2,z)*a2*c1*c2 - S(2,2,z)*a2*c1^2 - 2*S(2,2,z)*a1* d2^2 - 3*S(2,2,z)*a1*d1*d2 - 2*S(2,2,z)*a1*d1^2 + 3*S(2,2,z)*a1*c3*d2 + 3*S(2,2,z)*a1*c3*d1 - S(2,2,z)*a1*c3^2 + 3*S(2,2,z)*a1*c2*d2 + 3* S(2,2,z)*a1*c2*d1 - 3*S(2,2,z)*a1*c2*c3 - S(2,2,z)*a1*c2^2 + 3*S(2,2, z)*a1*c1*d2 + 3*S(2,2,z)*a1*c1*d1 - 3*S(2,2,z)*a1*c1*c3 - 3*S(2,2,z)* a1*c1*c2 - S(2,2,z)*a1*c1^2 - 2*S(2,2,z)*a1*a2*d2 - 2*S(2,2,z)*a1*a2* d1 + 2*S(2,2,z)*a1*a2*c3 + 2*S(2,2,z)*a1*a2*c2 + 2*S(2,2,z)*a1*a2*c1 + 1/24*ln(1 - z)^4*d2^3 + 1/8*ln(1 - z)^4*d1*d2^2 + 1/8*ln(1 - z)^4* d1^2*d2 + 1/24*ln(1 - z)^4*d1^3 - 1/8*ln(1 - z)^4*c3*d2^2 - 1/4*ln(1 - z)^4*c3*d1*d2 - 1/8*ln(1 - z)^4*c3*d1^2 + 1/8*ln(1 - z)^4*c3^2*d2 + 1/8*ln(1 - z)^4*c3^2*d1 - 1/24*ln(1 - z)^4*c3^3 - 1/8*ln(1 - z)^4* c2*d2^2 - 1/4*ln(1 - z)^4*c2*d1*d2 - 1/8*ln(1 - z)^4*c2*d1^2 + 1/4* ln(1 - z)^4*c2*c3*d2 + 1/4*ln(1 - z)^4*c2*c3*d1 - 1/8*ln(1 - z)^4*c2* c3^2 + 1/8*ln(1 - z)^4*c2^2*d2 + 1/8*ln(1 - z)^4*c2^2*d1 - 1/8*ln(1 - z)^4*c2^2*c3 - 1/24*ln(1 - z)^4*c2^3 - 1/8*ln(1 - z)^4*c1*d2^2 - 1/ 4*ln(1 - z)^4*c1*d1*d2 - 1/8*ln(1 - z)^4*c1*d1^2 + 1/4*ln(1 - z)^4*c1 *c3*d2 + 1/4*ln(1 - z)^4*c1*c3*d1 - 1/8*ln(1 - z)^4*c1*c3^2 + 1/4*ln( 1 - z)^4*c1*c2*d2 + 1/4*ln(1 - z)^4*c1*c2*d1 - 1/4*ln(1 - z)^4*c1*c2* c3 - 1/8*ln(1 - z)^4*c1*c2^2 + 1/8*ln(1 - z)^4*c1^2*d2 + 1/8*ln(1 - z )^4*c1^2*d1 - 1/8*ln(1 - z)^4*c1^2*c3 - 1/8*ln(1 - z)^4*c1^2*c2 - 1/ 24*ln(1 - z)^4*c1^3 + 1/8*ln(1 - z)^4*a2*d2^2 + 1/4*ln(1 - z)^4*a2*d1 *d2 + 1/8*ln(1 - z)^4*a2*d1^2 - 1/4*ln(1 - z)^4*a2*c3*d2 - 1/4*ln(1 - z)^4*a2*c3*d1 + 1/8*ln(1 - z)^4*a2*c3^2 - 1/4*ln(1 - z)^4*a2*c2*d2 - 1/4*ln(1 - z)^4*a2*c2*d1 + 1/4*ln(1 - z)^4*a2*c2*c3 + 1/8*ln(1 - z )^4*a2*c2^2 - 1/4*ln(1 - z)^4*a2*c1*d2 - 1/4*ln(1 - z)^4*a2*c1*d1 + 1/ 4*ln(1 - z)^4*a2*c1*c3 + 1/4*ln(1 - z)^4*a2*c1*c2 + 1/8*ln(1 - z)^4* a2*c1^2 + 1/8*ln(1 - z)^4*a2^2*d2 + 1/8*ln(1 - z)^4*a2^2*d1 - 1/8*ln( 1 - z)^4*a2^2*c3 - 1/8*ln(1 - z)^4*a2^2*c2 - 1/8*ln(1 - z)^4*a2^2*c1 + 1/24*ln(1 - z)^4*a2^3 + 1/8*ln(1 - z)^4*a1*d2^2 + 1/4*ln(1 - z)^4* a1*d1*d2 + 1/8*ln(1 - z)^4*a1*d1^2 - 1/4*ln(1 - z)^4*a1*c3*d2 - 1/4* ln(1 - z)^4*a1*c3*d1 + 1/8*ln(1 - z)^4*a1*c3^2 - 1/4*ln(1 - z)^4*a1* c2*d2 - 1/4*ln(1 - z)^4*a1*c2*d1 + 1/4*ln(1 - z)^4*a1*c2*c3 + 1/8*ln( 1 - z)^4*a1*c2^2 - 1/4*ln(1 - z)^4*a1*c1*d2 - 1/4*ln(1 - z)^4*a1*c1* d1 + 1/4*ln(1 - z)^4*a1*c1*c3 + 1/4*ln(1 - z)^4*a1*c1*c2 + 1/8*ln(1 - z)^4*a1*c1^2 + 1/4*ln(1 - z)^4*a1*a2*d2 + 1/4*ln(1 - z)^4*a1*a2*d1 - 1/4*ln(1 - z)^4*a1*a2*c3 - 1/4*ln(1 - z)^4*a1*a2*c2 - 1/4*ln(1 - z )^4*a1*a2*c1 + 1/8*ln(1 - z)^4*a1*a2^2 + 1/8*ln(1 - z)^4*a1^2*d2 + 1/ 8*ln(1 - z)^4*a1^2*d1 - 1/8*ln(1 - z)^4*a1^2*c3 - 1/8*ln(1 - z)^4* a1^2*c2 - 1/8*ln(1 - z)^4*a1^2*c1 + 1/8*ln(1 - z)^4*a1^2*a2 + 1/24* ln(1 - z)^4*a1^3 + 1/2*ln(1 - z)^2*Li(2,z)*d1*d2^2 + 1/2*ln(1 - z)^2* Li(2,z)*d1^2*d2 - 1/2*ln(1 - z)^2*Li(2,z)*c3*d2^2 - 3/2*ln(1 - z)^2* Li(2,z)*c3*d1*d2 - 1/2*ln(1 - z)^2*Li(2,z)*c3*d1^2 + ln(1 - z)^2*Li(2 ,z)*c3^2*d2 + ln(1 - z)^2*Li(2,z)*c3^2*d1 - 1/2*ln(1 - z)^2*Li(2,z)* c3^3 - 1/2*ln(1 - z)^2*Li(2,z)*c2*d2^2 - 3/2*ln(1 - z)^2*Li(2,z)*c2* d1*d2 - 1/2*ln(1 - z)^2*Li(2,z)*c2*d1^2 + 3/2*ln(1 - z)^2*Li(2,z)*c2* c3*d2 + 3/2*ln(1 - z)^2*Li(2,z)*c2*c3*d1 - ln(1 - z)^2*Li(2,z)*c2* c3^2 + ln(1 - z)^2*Li(2,z)*c2^2*d2 + ln(1 - z)^2*Li(2,z)*c2^2*d1 - ln(1 - z)^2*Li(2,z)*c2^2*c3 - 1/2*ln(1 - z)^2*Li(2,z)*c2^3 - 1/2*ln(1 - z)^2*Li(2,z)*c1*d2^2 - 3/2*ln(1 - z)^2*Li(2,z)*c1*d1*d2 - 1/2*ln(1 - z)^2*Li(2,z)*c1*d1^2 + 3/2*ln(1 - z)^2*Li(2,z)*c1*c3*d2 + 3/2*ln(1 - z)^2*Li(2,z)*c1*c3*d1 - ln(1 - z)^2*Li(2,z)*c1*c3^2 + 3/2*ln(1 - z )^2*Li(2,z)*c1*c2*d2 + 3/2*ln(1 - z)^2*Li(2,z)*c1*c2*d1 - 3/2*ln(1 - z)^2*Li(2,z)*c1*c2*c3 - ln(1 - z)^2*Li(2,z)*c1*c2^2 + ln(1 - z)^2*Li( 2,z)*c1^2*d2 + ln(1 - z)^2*Li(2,z)*c1^2*d1 - ln(1 - z)^2*Li(2,z)*c1^2 *c3 - ln(1 - z)^2*Li(2,z)*c1^2*c2 - 1/2*ln(1 - z)^2*Li(2,z)*c1^3 + 1/ 2*ln(1 - z)^2*Li(2,z)*a2*d2^2 + 3/2*ln(1 - z)^2*Li(2,z)*a2*d1*d2 + 1/ 2*ln(1 - z)^2*Li(2,z)*a2*d1^2 - 3/2*ln(1 - z)^2*Li(2,z)*a2*c3*d2 - 3/ 2*ln(1 - z)^2*Li(2,z)*a2*c3*d1 + ln(1 - z)^2*Li(2,z)*a2*c3^2 - 3/2* ln(1 - z)^2*Li(2,z)*a2*c2*d2 - 3/2*ln(1 - z)^2*Li(2,z)*a2*c2*d1 + 3/2 *ln(1 - z)^2*Li(2,z)*a2*c2*c3 + ln(1 - z)^2*Li(2,z)*a2*c2^2 - 3/2*ln( 1 - z)^2*Li(2,z)*a2*c1*d2 - 3/2*ln(1 - z)^2*Li(2,z)*a2*c1*d1 + 3/2* ln(1 - z)^2*Li(2,z)*a2*c1*c3 + 3/2*ln(1 - z)^2*Li(2,z)*a2*c1*c2 + ln( 1 - z)^2*Li(2,z)*a2*c1^2 + 1/2*ln(1 - z)^2*Li(2,z)*a2^2*d2 + 1/2*ln(1 - z)^2*Li(2,z)*a2^2*d1 - 1/2*ln(1 - z)^2*Li(2,z)*a2^2*c3 - 1/2*ln(1 - z)^2*Li(2,z)*a2^2*c2 - 1/2*ln(1 - z)^2*Li(2,z)*a2^2*c1 + 1/2*ln(1 - z)^2*Li(2,z)*a1*d2^2 + 3/2*ln(1 - z)^2*Li(2,z)*a1*d1*d2 + 1/2*ln(1 - z)^2*Li(2,z)*a1*d1^2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*c3*d2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*c3*d1 + ln(1 - z)^2*Li(2,z)*a1*c3^2 - 3/2*ln(1 - z )^2*Li(2,z)*a1*c2*d2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*c2*d1 + 3/2*ln(1 - z)^2*Li(2,z)*a1*c2*c3 + ln(1 - z)^2*Li(2,z)*a1*c2^2 - 3/2*ln(1 - z)^2 *Li(2,z)*a1*c1*d2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*c1*d1 + 3/2*ln(1 - z)^ 2*Li(2,z)*a1*c1*c3 + 3/2*ln(1 - z)^2*Li(2,z)*a1*c1*c2 + ln(1 - z)^2* Li(2,z)*a1*c1^2 + 3/2*ln(1 - z)^2*Li(2,z)*a1*a2*d2 + 3/2*ln(1 - z)^2* Li(2,z)*a1*a2*d1 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a2*c3 - 3/2*ln(1 - z)^2 *Li(2,z)*a1*a2*c2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a2*c1 + 1/2*ln(1 - z)^ 2*Li(2,z)*a1*a2^2 + 1/2*ln(1 - z)^2*Li(2,z)*a1^2*d2 + 1/2*ln(1 - z)^2 *Li(2,z)*a1^2*d1 - 1/2*ln(1 - z)^2*Li(2,z)*a1^2*c3 - 1/2*ln(1 - z)^2* Li(2,z)*a1^2*c2 - 1/2*ln(1 - z)^2*Li(2,z)*a1^2*c1 + 1/2*ln(1 - z)^2* Li(2,z)*a1^2*a2 + ln(1 - z)*Li(3,z)*c3*d1*d2 - ln(1 - z)*Li(3,z)*c3^2 *d2 - ln(1 - z)*Li(3,z)*c3^2*d1 + ln(1 - z)*Li(3,z)*c3^3 + ln(1 - z)* Li(3,z)*c2*d1*d2 - ln(1 - z)*Li(3,z)*c2*c3*d2 - ln(1 - z)*Li(3,z)*c2* c3*d1 + ln(1 - z)*Li(3,z)*c2*c3^2 - ln(1 - z)*Li(3,z)*c2^2*d2 - ln(1 - z)*Li(3,z)*c2^2*d1 + ln(1 - z)*Li(3,z)*c2^2*c3 + ln(1 - z)*Li(3,z) *c2^3 + ln(1 - z)*Li(3,z)*c1*d1*d2 - ln(1 - z)*Li(3,z)*c1*c3*d2 - ln( 1 - z)*Li(3,z)*c1*c3*d1 + ln(1 - z)*Li(3,z)*c1*c3^2 - ln(1 - z)*Li(3, z)*c1*c2*d2 - ln(1 - z)*Li(3,z)*c1*c2*d1 + ln(1 - z)*Li(3,z)*c1*c2*c3 + ln(1 - z)*Li(3,z)*c1*c2^2 - ln(1 - z)*Li(3,z)*c1^2*d2 - ln(1 - z)* Li(3,z)*c1^2*d1 + ln(1 - z)*Li(3,z)*c1^2*c3 + ln(1 - z)*Li(3,z)*c1^2* c2 + ln(1 - z)*Li(3,z)*c1^3 - ln(1 - z)*Li(3,z)*a2*d1*d2 + ln(1 - z)* Li(3,z)*a2*c3*d2 + ln(1 - z)*Li(3,z)*a2*c3*d1 - ln(1 - z)*Li(3,z)*a2* c3^2 + ln(1 - z)*Li(3,z)*a2*c2*d2 + ln(1 - z)*Li(3,z)*a2*c2*d1 - ln(1 - z)*Li(3,z)*a2*c2*c3 - ln(1 - z)*Li(3,z)*a2*c2^2 + ln(1 - z)*Li(3,z )*a2*c1*d2 + ln(1 - z)*Li(3,z)*a2*c1*d1 - ln(1 - z)*Li(3,z)*a2*c1*c3 - ln(1 - z)*Li(3,z)*a2*c1*c2 - ln(1 - z)*Li(3,z)*a2*c1^2 - ln(1 - z) *Li(3,z)*a1*d1*d2 + ln(1 - z)*Li(3,z)*a1*c3*d2 + ln(1 - z)*Li(3,z)*a1 *c3*d1 - ln(1 - z)*Li(3,z)*a1*c3^2 + ln(1 - z)*Li(3,z)*a1*c2*d2 + ln( 1 - z)*Li(3,z)*a1*c2*d1 - ln(1 - z)*Li(3,z)*a1*c2*c3 - ln(1 - z)*Li(3 ,z)*a1*c2^2 + ln(1 - z)*Li(3,z)*a1*c1*d2 + ln(1 - z)*Li(3,z)*a1*c1*d1 - ln(1 - z)*Li(3,z)*a1*c1*c3 - ln(1 - z)*Li(3,z)*a1*c1*c2 - ln(1 - z )*Li(3,z)*a1*c1^2 - ln(1 - z)*Li(3,z)*a1*a2*d2 - ln(1 - z)*Li(3,z)*a1 *a2*d1 + ln(1 - z)*Li(3,z)*a1*a2*c3 + ln(1 - z)*Li(3,z)*a1*a2*c2 + ln(1 - z)*Li(3,z)*a1*a2*c1 + 1/2*Li(2,z)^2*d1*d2^2 + 1/2*Li(2,z)^2* d1^2*d2 - 1/2*Li(2,z)^2*c3*d2^2 - Li(2,z)^2*c3*d1*d2 - 1/2*Li(2,z)^2* c3*d1^2 + 1/2*Li(2,z)^2*c3^2*d2 + 1/2*Li(2,z)^2*c3^2*d1 - 1/2*Li(2,z) ^2*c2*d2^2 - Li(2,z)^2*c2*d1*d2 - 1/2*Li(2,z)^2*c2*d1^2 + Li(2,z)^2* c2*c3*d2 + Li(2,z)^2*c2*c3*d1 - 1/2*Li(2,z)^2*c2*c3^2 + 1/2*Li(2,z)^2 *c2^2*d2 + 1/2*Li(2,z)^2*c2^2*d1 - 1/2*Li(2,z)^2*c2^2*c3 - 1/2*Li(2,z )^2*c1*d2^2 - Li(2,z)^2*c1*d1*d2 - 1/2*Li(2,z)^2*c1*d1^2 + Li(2,z)^2* c1*c3*d2 + Li(2,z)^2*c1*c3*d1 - 1/2*Li(2,z)^2*c1*c3^2 + Li(2,z)^2*c1* c2*d2 + Li(2,z)^2*c1*c2*d1 - Li(2,z)^2*c1*c2*c3 - 1/2*Li(2,z)^2*c1* c2^2 + 1/2*Li(2,z)^2*c1^2*d2 + 1/2*Li(2,z)^2*c1^2*d1 - 1/2*Li(2,z)^2* c1^2*c3 - 1/2*Li(2,z)^2*c1^2*c2 + 1/2*Li(2,z)^2*a2*d2^2 + 1/2*Li(2,z) ^2*a2*d1*d2 + 1/2*Li(2,z)^2*a2*d1^2 - 1/2*Li(2,z)^2*a2*c3*d2 - 1/2* Li(2,z)^2*a2*c3*d1 - 1/2*Li(2,z)^2*a2*c2*d2 - 1/2*Li(2,z)^2*a2*c2*d1 + 1/2*Li(2,z)^2*a2*c2*c3 - 1/2*Li(2,z)^2*a2*c1*d2 - 1/2*Li(2,z)^2*a2 *c1*d1 + 1/2*Li(2,z)^2*a2*c1*c3 + 1/2*Li(2,z)^2*a2*c1*c2 + 1/2*Li(2,z )^2*a1*d2^2 + 1/2*Li(2,z)^2*a1*d1*d2 + 1/2*Li(2,z)^2*a1*d1^2 - 1/2* Li(2,z)^2*a1*c3*d2 - 1/2*Li(2,z)^2*a1*c3*d1 - 1/2*Li(2,z)^2*a1*c2*d2 - 1/2*Li(2,z)^2*a1*c2*d1 + 1/2*Li(2,z)^2*a1*c2*c3 - 1/2*Li(2,z)^2*a1 *c1*d2 - 1/2*Li(2,z)^2*a1*c1*d1 + 1/2*Li(2,z)^2*a1*c1*c3 + 1/2*Li(2,z )^2*a1*c1*c2 - Li(4,z)*c3*d1*d2 + Li(4,z)*c3^2*d2 + Li(4,z)*c3^2*d1 - Li(4,z)*c3^3 - Li(4,z)*c2*d1*d2 + Li(4,z)*c2*c3*d2 + Li(4,z)*c2*c3 *d1 - Li(4,z)*c2*c3^2 + Li(4,z)*c2^2*d2 + Li(4,z)*c2^2*d1 - Li(4,z)* c2^2*c3 - Li(4,z)*c2^3 - Li(4,z)*c1*d1*d2 + Li(4,z)*c1*c3*d2 + Li(4,z )*c1*c3*d1 - Li(4,z)*c1*c3^2 + Li(4,z)*c1*c2*d2 + Li(4,z)*c1*c2*d1 - Li(4,z)*c1*c2*c3 - Li(4,z)*c1*c2^2 + Li(4,z)*c1^2*d2 + Li(4,z)*c1^2* d1 - Li(4,z)*c1^2*c3 - Li(4,z)*c1^2*c2 - Li(4,z)*c1^3 ) + ep^4*FI43C(a1,a2,d1,d2,c1,c2,c3,z,ep^4) ); .sort **************************************************************************************** * * FI43D = Hypergeometric4F3[1+a1*ep, 1+a2*ep, 1+a3*ep, 1+a4*ep; 2+c1*ep, 2+c2*ep, 1+e1*ep;z] * **************************************************************************************** id FI43D(a1?,a2?,a3?,a4?,c1?,c2?,e1?,z?,ep?) = 1/z^2*[1+c1*ep]*[1+c2*ep]*( + Li(2,z) + ep * ( - S(1,2,z)*e1 - S(1,2,z)*c2 - S(1,2,z)*c1 + S(1,2,z)*a4 + S(1 ,2,z)*a3 + S(1,2,z)*a2 + S(1,2,z)*a1 - Li(3,z)*c2 - Li(3,z)*c1 ) + ep^2 * ( S(1,3,z)*e1^2 + 2*S(1,3,z)*c2*e1 + S(1,3,z)*c2^2 + 2*S(1,3,z )*c1*e1 + 2*S(1,3,z)*c1*c2 + S(1,3,z)*c1^2 - 2*S(1,3,z)*a4*e1 - 2*S(1 ,3,z)*a4*c2 - 2*S(1,3,z)*a4*c1 + S(1,3,z)*a4^2 - 2*S(1,3,z)*a3*e1 - 2 *S(1,3,z)*a3*c2 - 2*S(1,3,z)*a3*c1 + 2*S(1,3,z)*a3*a4 + S(1,3,z)*a3^2 - 2*S(1,3,z)*a2*e1 - 2*S(1,3,z)*a2*c2 - 2*S(1,3,z)*a2*c1 + 2*S(1,3,z )*a2*a4 + 2*S(1,3,z)*a2*a3 + S(1,3,z)*a2^2 - 2*S(1,3,z)*a1*e1 - 2*S(1 ,3,z)*a1*c2 - 2*S(1,3,z)*a1*c1 + 2*S(1,3,z)*a1*a4 + 2*S(1,3,z)*a1*a3 + 2*S(1,3,z)*a1*a2 + S(1,3,z)*a1^2 - 2*S(2,2,z)*e1^2 - S(2,2,z)*c2* e1 - S(2,2,z)*c2^2 - S(2,2,z)*c1*e1 - S(2,2,z)*c1^2 + 2*S(2,2,z)*a4* e1 + S(2,2,z)*a4*c2 + S(2,2,z)*a4*c1 + 2*S(2,2,z)*a3*e1 + S(2,2,z)*a3 *c2 + S(2,2,z)*a3*c1 - 2*S(2,2,z)*a3*a4 + 2*S(2,2,z)*a2*e1 + S(2,2,z) *a2*c2 + S(2,2,z)*a2*c1 - 2*S(2,2,z)*a2*a4 - 2*S(2,2,z)*a2*a3 + 2*S(2 ,2,z)*a1*e1 + S(2,2,z)*a1*c2 + S(2,2,z)*a1*c1 - 2*S(2,2,z)*a1*a4 - 2* S(2,2,z)*a1*a3 - 2*S(2,2,z)*a1*a2 + 1/2*Li(2,z)^2*e1^2 + 1/2*Li(2,z)^ 2*c2*e1 + 1/2*Li(2,z)^2*c2^2 + 1/2*Li(2,z)^2*c1*e1 + 1/2*Li(2,z)^2*c1 *c2 + 1/2*Li(2,z)^2*c1^2 - 1/2*Li(2,z)^2*a4*e1 - 1/2*Li(2,z)^2*a4*c2 - 1/2*Li(2,z)^2*a4*c1 - 1/2*Li(2,z)^2*a3*e1 - 1/2*Li(2,z)^2*a3*c2 - 1/2*Li(2,z)^2*a3*c1 + 1/2*Li(2,z)^2*a3*a4 - 1/2*Li(2,z)^2*a2*e1 - 1/2 *Li(2,z)^2*a2*c2 - 1/2*Li(2,z)^2*a2*c1 + 1/2*Li(2,z)^2*a2*a4 + 1/2* Li(2,z)^2*a2*a3 - 1/2*Li(2,z)^2*a1*e1 - 1/2*Li(2,z)^2*a1*c2 - 1/2*Li( 2,z)^2*a1*c1 + 1/2*Li(2,z)^2*a1*a4 + 1/2*Li(2,z)^2*a1*a3 + 1/2*Li(2,z )^2*a1*a2 + Li(4,z)*c2^2 + Li(4,z)*c1*c2 + Li(4,z)*c1^2 ) + ep^3*FI43D(a1,a2,a3,a4,c1,c2,e1,z,ep^3) ); .sort **************************************************************************************** * * FI43E = Hypergeometric3F2[1+a1*ep,1+a2*ep,1+a3*ep,1+a4*ep; 2+c1*ep, 1+e1*ep, 1+e2*ep;z] * **************************************************************************************** id FI43E(a1?,a2?,a3?,a4?,c1?,e1?,e2?,z?,ep?) = 1/z*[1+c1*ep]*( - ln(1 - z) + ep * ( - 1/2*ln(1 - z)^2*e2 - 1/2*ln(1 - z)^2*e1 - 1/2*ln(1 - z)^2* c1 + 1/2*ln(1 - z)^2*a4 + 1/2*ln(1 - z)^2*a3 + 1/2*ln(1 - z)^2*a2 + 1/ 2*ln(1 - z)^2*a1 - Li(2,z)*c1 ) + ep^2 * ( - 2*S(1,2,z)*e2^2 - 2*S(1,2,z)*e1*e2 - 2*S(1,2,z)*e1^2 - S( 1,2,z)*c1*e2 - S(1,2,z)*c1*e1 - S(1,2,z)*c1^2 + 2*S(1,2,z)*a4*e2 + 2* S(1,2,z)*a4*e1 + S(1,2,z)*a4*c1 + 2*S(1,2,z)*a3*e2 + 2*S(1,2,z)*a3*e1 + S(1,2,z)*a3*c1 - 2*S(1,2,z)*a3*a4 + 2*S(1,2,z)*a2*e2 + 2*S(1,2,z)* a2*e1 + S(1,2,z)*a2*c1 - 2*S(1,2,z)*a2*a4 - 2*S(1,2,z)*a2*a3 + 2*S(1, 2,z)*a1*e2 + 2*S(1,2,z)*a1*e1 + S(1,2,z)*a1*c1 - 2*S(1,2,z)*a1*a4 - 2 *S(1,2,z)*a1*a3 - 2*S(1,2,z)*a1*a2 - 1/6*ln(1 - z)^3*e2^2 - 1/3*ln(1 - z)^3*e1*e2 - 1/6*ln(1 - z)^3*e1^2 - 1/3*ln(1 - z)^3*c1*e2 - 1/3* ln(1 - z)^3*c1*e1 - 1/6*ln(1 - z)^3*c1^2 + 1/3*ln(1 - z)^3*a4*e2 + 1/ 3*ln(1 - z)^3*a4*e1 + 1/3*ln(1 - z)^3*a4*c1 - 1/6*ln(1 - z)^3*a4^2 + 1/3*ln(1 - z)^3*a3*e2 + 1/3*ln(1 - z)^3*a3*e1 + 1/3*ln(1 - z)^3*a3*c1 - 1/3*ln(1 - z)^3*a3*a4 - 1/6*ln(1 - z)^3*a3^2 + 1/3*ln(1 - z)^3*a2* e2 + 1/3*ln(1 - z)^3*a2*e1 + 1/3*ln(1 - z)^3*a2*c1 - 1/3*ln(1 - z)^3* a2*a4 - 1/3*ln(1 - z)^3*a2*a3 - 1/6*ln(1 - z)^3*a2^2 + 1/3*ln(1 - z)^ 3*a1*e2 + 1/3*ln(1 - z)^3*a1*e1 + 1/3*ln(1 - z)^3*a1*c1 - 1/3*ln(1 - z)^3*a1*a4 - 1/3*ln(1 - z)^3*a1*a3 - 1/3*ln(1 - z)^3*a1*a2 - 1/6*ln(1 - z)^3*a1^2 - ln(1 - z)*Li(2,z)*e2^2 - ln(1 - z)*Li(2,z)*e1*e2 - ln( 1 - z)*Li(2,z)*e1^2 - ln(1 - z)*Li(2,z)*c1*e2 - ln(1 - z)*Li(2,z)*c1* e1 - ln(1 - z)*Li(2,z)*c1^2 + ln(1 - z)*Li(2,z)*a4*e2 + ln(1 - z)*Li( 2,z)*a4*e1 + ln(1 - z)*Li(2,z)*a4*c1 + ln(1 - z)*Li(2,z)*a3*e2 + ln(1 - z)*Li(2,z)*a3*e1 + ln(1 - z)*Li(2,z)*a3*c1 - ln(1 - z)*Li(2,z)*a3* a4 + ln(1 - z)*Li(2,z)*a2*e2 + ln(1 - z)*Li(2,z)*a2*e1 + ln(1 - z)* Li(2,z)*a2*c1 - ln(1 - z)*Li(2,z)*a2*a4 - ln(1 - z)*Li(2,z)*a2*a3 + ln(1 - z)*Li(2,z)*a1*e2 + ln(1 - z)*Li(2,z)*a1*e1 + ln(1 - z)*Li(2,z) *a1*c1 - ln(1 - z)*Li(2,z)*a1*a4 - ln(1 - z)*Li(2,z)*a1*a3 - ln(1 - z )*Li(2,z)*a1*a2 + Li(3,z)*c1^2 ) + ep^3 * ( - S(1,2,z)*ln(1 - z)*e2^3 - 2*S(1,2,z)*ln(1 - z)*e1*e2^2 - 2*S(1,2,z)*ln(1 - z)*e1^2*e2 - S(1,2,z)*ln(1 - z)*e1^3 - 2*S(1,2,z)* ln(1 - z)*c1*e2^2 - 3*S(1,2,z)*ln(1 - z)*c1*e1*e2 - 2*S(1,2,z)*ln(1 - z)*c1*e1^2 - 2*S(1,2,z)*ln(1 - z)*c1^2*e2 - 2*S(1,2,z)*ln(1 - z)* c1^2*e1 - S(1,2,z)*ln(1 - z)*c1^3 + 2*S(1,2,z)*ln(1 - z)*a4*e2^2 + 3* S(1,2,z)*ln(1 - z)*a4*e1*e2 + 2*S(1,2,z)*ln(1 - z)*a4*e1^2 + 3*S(1,2, z)*ln(1 - z)*a4*c1*e2 + 3*S(1,2,z)*ln(1 - z)*a4*c1*e1 + 2*S(1,2,z)* ln(1 - z)*a4*c1^2 - S(1,2,z)*ln(1 - z)*a4^2*e2 - S(1,2,z)*ln(1 - z)* a4^2*e1 - S(1,2,z)*ln(1 - z)*a4^2*c1 + 2*S(1,2,z)*ln(1 - z)*a3*e2^2 + 3*S(1,2,z)*ln(1 - z)*a3*e1*e2 + 2*S(1,2,z)*ln(1 - z)*a3*e1^2 + 3* S(1,2,z)*ln(1 - z)*a3*c1*e2 + 3*S(1,2,z)*ln(1 - z)*a3*c1*e1 + 2*S(1,2 ,z)*ln(1 - z)*a3*c1^2 - 3*S(1,2,z)*ln(1 - z)*a3*a4*e2 - 3*S(1,2,z)* ln(1 - z)*a3*a4*e1 - 3*S(1,2,z)*ln(1 - z)*a3*a4*c1 + S(1,2,z)*ln(1 - z)*a3*a4^2 - S(1,2,z)*ln(1 - z)*a3^2*e2 - S(1,2,z)*ln(1 - z)*a3^2*e1 - S(1,2,z)*ln(1 - z)*a3^2*c1 + S(1,2,z)*ln(1 - z)*a3^2*a4 + 2*S(1,2, z)*ln(1 - z)*a2*e2^2 + 3*S(1,2,z)*ln(1 - z)*a2*e1*e2 + 2*S(1,2,z)*ln( 1 - z)*a2*e1^2 + 3*S(1,2,z)*ln(1 - z)*a2*c1*e2 + 3*S(1,2,z)*ln(1 - z) *a2*c1*e1 + 2*S(1,2,z)*ln(1 - z)*a2*c1^2 - 3*S(1,2,z)*ln(1 - z)*a2*a4 *e2 - 3*S(1,2,z)*ln(1 - z)*a2*a4*e1 - 3*S(1,2,z)*ln(1 - z)*a2*a4*c1 + S(1,2,z)*ln(1 - z)*a2*a4^2 - 3*S(1,2,z)*ln(1 - z)*a2*a3*e2 - 3*S(1 ,2,z)*ln(1 - z)*a2*a3*e1 - 3*S(1,2,z)*ln(1 - z)*a2*a3*c1 + 3*S(1,2,z) *ln(1 - z)*a2*a3*a4 + S(1,2,z)*ln(1 - z)*a2*a3^2 - S(1,2,z)*ln(1 - z) *a2^2*e2 - S(1,2,z)*ln(1 - z)*a2^2*e1 - S(1,2,z)*ln(1 - z)*a2^2*c1 + S(1,2,z)*ln(1 - z)*a2^2*a4 + S(1,2,z)*ln(1 - z)*a2^2*a3 + 2*S(1,2,z)* ln(1 - z)*a1*e2^2 + 3*S(1,2,z)*ln(1 - z)*a1*e1*e2 + 2*S(1,2,z)*ln(1 - z)*a1*e1^2 + 3*S(1,2,z)*ln(1 - z)*a1*c1*e2 + 3*S(1,2,z)*ln(1 - z)* a1*c1*e1 + 2*S(1,2,z)*ln(1 - z)*a1*c1^2 - 3*S(1,2,z)*ln(1 - z)*a1*a4* e2 - 3*S(1,2,z)*ln(1 - z)*a1*a4*e1 - 3*S(1,2,z)*ln(1 - z)*a1*a4*c1 + S(1,2,z)*ln(1 - z)*a1*a4^2 - 3*S(1,2,z)*ln(1 - z)*a1*a3*e2 - 3*S(1,2, z)*ln(1 - z)*a1*a3*e1 - 3*S(1,2,z)*ln(1 - z)*a1*a3*c1 + 3*S(1,2,z)* ln(1 - z)*a1*a3*a4 + S(1,2,z)*ln(1 - z)*a1*a3^2 - 3*S(1,2,z)*ln(1 - z )*a1*a2*e2 - 3*S(1,2,z)*ln(1 - z)*a1*a2*e1 - 3*S(1,2,z)*ln(1 - z)*a1* a2*c1 + 3*S(1,2,z)*ln(1 - z)*a1*a2*a4 + 3*S(1,2,z)*ln(1 - z)*a1*a2*a3 + S(1,2,z)*ln(1 - z)*a1*a2^2 - S(1,2,z)*ln(1 - z)*a1^2*e2 - S(1,2,z) *ln(1 - z)*a1^2*e1 - S(1,2,z)*ln(1 - z)*a1^2*c1 + S(1,2,z)*ln(1 - z)* a1^2*a4 + S(1,2,z)*ln(1 - z)*a1^2*a3 + S(1,2,z)*ln(1 - z)*a1^2*a2 - S(1,3,z)*c1*e2^2 - 2*S(1,3,z)*c1*e1*e2 - S(1,3,z)*c1*e1^2 - 2*S(1,3,z )*c1^2*e2 - 2*S(1,3,z)*c1^2*e1 - S(1,3,z)*c1^3 + 2*S(1,3,z)*a4*c1*e2 + 2*S(1,3,z)*a4*c1*e1 + 2*S(1,3,z)*a4*c1^2 - S(1,3,z)*a4^2*c1 + 2*S( 1,3,z)*a3*c1*e2 + 2*S(1,3,z)*a3*c1*e1 + 2*S(1,3,z)*a3*c1^2 - 2*S(1,3, z)*a3*a4*c1 - S(1,3,z)*a3^2*c1 + 2*S(1,3,z)*a2*c1*e2 + 2*S(1,3,z)*a2* c1*e1 + 2*S(1,3,z)*a2*c1^2 - 2*S(1,3,z)*a2*a4*c1 - 2*S(1,3,z)*a2*a3* c1 - S(1,3,z)*a2^2*c1 + 2*S(1,3,z)*a1*c1*e2 + 2*S(1,3,z)*a1*c1*e1 + 2 *S(1,3,z)*a1*c1^2 - 2*S(1,3,z)*a1*a4*c1 - 2*S(1,3,z)*a1*a3*c1 - 2*S(1 ,3,z)*a1*a2*c1 - S(1,3,z)*a1^2*c1 + 2*S(2,2,z)*c1*e2^2 + 2*S(2,2,z)* c1*e1*e2 + 2*S(2,2,z)*c1*e1^2 + S(2,2,z)*c1^2*e2 + S(2,2,z)*c1^2*e1 + S(2,2,z)*c1^3 - 2*S(2,2,z)*a4*c1*e2 - 2*S(2,2,z)*a4*c1*e1 - S(2,2, z)*a4*c1^2 - 2*S(2,2,z)*a3*c1*e2 - 2*S(2,2,z)*a3*c1*e1 - S(2,2,z)*a3* c1^2 + 2*S(2,2,z)*a3*a4*c1 - 2*S(2,2,z)*a2*c1*e2 - 2*S(2,2,z)*a2*c1* e1 - S(2,2,z)*a2*c1^2 + 2*S(2,2,z)*a2*a4*c1 + 2*S(2,2,z)*a2*a3*c1 - 2 *S(2,2,z)*a1*c1*e2 - 2*S(2,2,z)*a1*c1*e1 - S(2,2,z)*a1*c1^2 + 2*S(2,2 ,z)*a1*a4*c1 + 2*S(2,2,z)*a1*a3*c1 + 2*S(2,2,z)*a1*a2*c1 - 1/24*ln(1 - z)^4*e2^3 - 1/8*ln(1 - z)^4*e1*e2^2 - 1/8*ln(1 - z)^4*e1^2*e2 - 1/ 24*ln(1 - z)^4*e1^3 - 1/8*ln(1 - z)^4*c1*e2^2 - 1/4*ln(1 - z)^4*c1*e1 *e2 - 1/8*ln(1 - z)^4*c1*e1^2 - 1/8*ln(1 - z)^4*c1^2*e2 - 1/8*ln(1 - z)^4*c1^2*e1 - 1/24*ln(1 - z)^4*c1^3 + 1/8*ln(1 - z)^4*a4*e2^2 + 1/4* ln(1 - z)^4*a4*e1*e2 + 1/8*ln(1 - z)^4*a4*e1^2 + 1/4*ln(1 - z)^4*a4* c1*e2 + 1/4*ln(1 - z)^4*a4*c1*e1 + 1/8*ln(1 - z)^4*a4*c1^2 - 1/8*ln(1 - z)^4*a4^2*e2 - 1/8*ln(1 - z)^4*a4^2*e1 - 1/8*ln(1 - z)^4*a4^2*c1 + 1/24*ln(1 - z)^4*a4^3 + 1/8*ln(1 - z)^4*a3*e2^2 + 1/4*ln(1 - z)^4* a3*e1*e2 + 1/8*ln(1 - z)^4*a3*e1^2 + 1/4*ln(1 - z)^4*a3*c1*e2 + 1/4* ln(1 - z)^4*a3*c1*e1 + 1/8*ln(1 - z)^4*a3*c1^2 - 1/4*ln(1 - z)^4*a3* a4*e2 - 1/4*ln(1 - z)^4*a3*a4*e1 - 1/4*ln(1 - z)^4*a3*a4*c1 + 1/8*ln( 1 - z)^4*a3*a4^2 - 1/8*ln(1 - z)^4*a3^2*e2 - 1/8*ln(1 - z)^4*a3^2*e1 - 1/8*ln(1 - z)^4*a3^2*c1 + 1/8*ln(1 - z)^4*a3^2*a4 + 1/24*ln(1 - z) ^4*a3^3 + 1/8*ln(1 - z)^4*a2*e2^2 + 1/4*ln(1 - z)^4*a2*e1*e2 + 1/8* ln(1 - z)^4*a2*e1^2 + 1/4*ln(1 - z)^4*a2*c1*e2 + 1/4*ln(1 - z)^4*a2* c1*e1 + 1/8*ln(1 - z)^4*a2*c1^2 - 1/4*ln(1 - z)^4*a2*a4*e2 - 1/4*ln(1 - z)^4*a2*a4*e1 - 1/4*ln(1 - z)^4*a2*a4*c1 + 1/8*ln(1 - z)^4*a2*a4^2 - 1/4*ln(1 - z)^4*a2*a3*e2 - 1/4*ln(1 - z)^4*a2*a3*e1 - 1/4*ln(1 - z )^4*a2*a3*c1 + 1/4*ln(1 - z)^4*a2*a3*a4 + 1/8*ln(1 - z)^4*a2*a3^2 - 1/ 8*ln(1 - z)^4*a2^2*e2 - 1/8*ln(1 - z)^4*a2^2*e1 - 1/8*ln(1 - z)^4* a2^2*c1 + 1/8*ln(1 - z)^4*a2^2*a4 + 1/8*ln(1 - z)^4*a2^2*a3 + 1/24* ln(1 - z)^4*a2^3 + 1/8*ln(1 - z)^4*a1*e2^2 + 1/4*ln(1 - z)^4*a1*e1*e2 + 1/8*ln(1 - z)^4*a1*e1^2 + 1/4*ln(1 - z)^4*a1*c1*e2 + 1/4*ln(1 - z) ^4*a1*c1*e1 + 1/8*ln(1 - z)^4*a1*c1^2 - 1/4*ln(1 - z)^4*a1*a4*e2 - 1/ 4*ln(1 - z)^4*a1*a4*e1 - 1/4*ln(1 - z)^4*a1*a4*c1 + 1/8*ln(1 - z)^4* a1*a4^2 - 1/4*ln(1 - z)^4*a1*a3*e2 - 1/4*ln(1 - z)^4*a1*a3*e1 - 1/4* ln(1 - z)^4*a1*a3*c1 + 1/4*ln(1 - z)^4*a1*a3*a4 + 1/8*ln(1 - z)^4*a1* a3^2 - 1/4*ln(1 - z)^4*a1*a2*e2 - 1/4*ln(1 - z)^4*a1*a2*e1 - 1/4*ln(1 - z)^4*a1*a2*c1 + 1/4*ln(1 - z)^4*a1*a2*a4 + 1/4*ln(1 - z)^4*a1*a2* a3 + 1/8*ln(1 - z)^4*a1*a2^2 - 1/8*ln(1 - z)^4*a1^2*e2 - 1/8*ln(1 - z )^4*a1^2*e1 - 1/8*ln(1 - z)^4*a1^2*c1 + 1/8*ln(1 - z)^4*a1^2*a4 + 1/8 *ln(1 - z)^4*a1^2*a3 + 1/8*ln(1 - z)^4*a1^2*a2 + 1/24*ln(1 - z)^4* a1^3 - 1/2*ln(1 - z)^2*Li(2,z)*e2^3 - ln(1 - z)^2*Li(2,z)*e1*e2^2 - ln(1 - z)^2*Li(2,z)*e1^2*e2 - 1/2*ln(1 - z)^2*Li(2,z)*e1^3 - ln(1 - z )^2*Li(2,z)*c1*e2^2 - 3/2*ln(1 - z)^2*Li(2,z)*c1*e1*e2 - ln(1 - z)^2* Li(2,z)*c1*e1^2 - ln(1 - z)^2*Li(2,z)*c1^2*e2 - ln(1 - z)^2*Li(2,z)* c1^2*e1 - 1/2*ln(1 - z)^2*Li(2,z)*c1^3 + ln(1 - z)^2*Li(2,z)*a4*e2^2 + 3/2*ln(1 - z)^2*Li(2,z)*a4*e1*e2 + ln(1 - z)^2*Li(2,z)*a4*e1^2 + 3/ 2*ln(1 - z)^2*Li(2,z)*a4*c1*e2 + 3/2*ln(1 - z)^2*Li(2,z)*a4*c1*e1 + ln(1 - z)^2*Li(2,z)*a4*c1^2 - 1/2*ln(1 - z)^2*Li(2,z)*a4^2*e2 - 1/2* ln(1 - z)^2*Li(2,z)*a4^2*e1 - 1/2*ln(1 - z)^2*Li(2,z)*a4^2*c1 + ln(1 - z)^2*Li(2,z)*a3*e2^2 + 3/2*ln(1 - z)^2*Li(2,z)*a3*e1*e2 + ln(1 - z )^2*Li(2,z)*a3*e1^2 + 3/2*ln(1 - z)^2*Li(2,z)*a3*c1*e2 + 3/2*ln(1 - z )^2*Li(2,z)*a3*c1*e1 + ln(1 - z)^2*Li(2,z)*a3*c1^2 - 3/2*ln(1 - z)^2* Li(2,z)*a3*a4*e2 - 3/2*ln(1 - z)^2*Li(2,z)*a3*a4*e1 - 3/2*ln(1 - z)^2 *Li(2,z)*a3*a4*c1 + 1/2*ln(1 - z)^2*Li(2,z)*a3*a4^2 - 1/2*ln(1 - z)^2 *Li(2,z)*a3^2*e2 - 1/2*ln(1 - z)^2*Li(2,z)*a3^2*e1 - 1/2*ln(1 - z)^2* Li(2,z)*a3^2*c1 + 1/2*ln(1 - z)^2*Li(2,z)*a3^2*a4 + ln(1 - z)^2*Li(2, z)*a2*e2^2 + 3/2*ln(1 - z)^2*Li(2,z)*a2*e1*e2 + ln(1 - z)^2*Li(2,z)* a2*e1^2 + 3/2*ln(1 - z)^2*Li(2,z)*a2*c1*e2 + 3/2*ln(1 - z)^2*Li(2,z)* a2*c1*e1 + ln(1 - z)^2*Li(2,z)*a2*c1^2 - 3/2*ln(1 - z)^2*Li(2,z)*a2* a4*e2 - 3/2*ln(1 - z)^2*Li(2,z)*a2*a4*e1 - 3/2*ln(1 - z)^2*Li(2,z)*a2 *a4*c1 + 1/2*ln(1 - z)^2*Li(2,z)*a2*a4^2 - 3/2*ln(1 - z)^2*Li(2,z)*a2 *a3*e2 - 3/2*ln(1 - z)^2*Li(2,z)*a2*a3*e1 - 3/2*ln(1 - z)^2*Li(2,z)* a2*a3*c1 + 3/2*ln(1 - z)^2*Li(2,z)*a2*a3*a4 + 1/2*ln(1 - z)^2*Li(2,z) *a2*a3^2 - 1/2*ln(1 - z)^2*Li(2,z)*a2^2*e2 - 1/2*ln(1 - z)^2*Li(2,z)* a2^2*e1 - 1/2*ln(1 - z)^2*Li(2,z)*a2^2*c1 + 1/2*ln(1 - z)^2*Li(2,z)* a2^2*a4 + 1/2*ln(1 - z)^2*Li(2,z)*a2^2*a3 + ln(1 - z)^2*Li(2,z)*a1* e2^2 + 3/2*ln(1 - z)^2*Li(2,z)*a1*e1*e2 + ln(1 - z)^2*Li(2,z)*a1*e1^2 + 3/2*ln(1 - z)^2*Li(2,z)*a1*c1*e2 + 3/2*ln(1 - z)^2*Li(2,z)*a1*c1* e1 + ln(1 - z)^2*Li(2,z)*a1*c1^2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a4*e2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a4*e1 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a4* c1 + 1/2*ln(1 - z)^2*Li(2,z)*a1*a4^2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a3* e2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a3*e1 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a3 *c1 + 3/2*ln(1 - z)^2*Li(2,z)*a1*a3*a4 + 1/2*ln(1 - z)^2*Li(2,z)*a1* a3^2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a2*e2 - 3/2*ln(1 - z)^2*Li(2,z)*a1* a2*e1 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a2*c1 + 3/2*ln(1 - z)^2*Li(2,z)*a1 *a2*a4 + 3/2*ln(1 - z)^2*Li(2,z)*a1*a2*a3 + 1/2*ln(1 - z)^2*Li(2,z)* a1*a2^2 - 1/2*ln(1 - z)^2*Li(2,z)*a1^2*e2 - 1/2*ln(1 - z)^2*Li(2,z)* a1^2*e1 - 1/2*ln(1 - z)^2*Li(2,z)*a1^2*c1 + 1/2*ln(1 - z)^2*Li(2,z)* a1^2*a4 + 1/2*ln(1 - z)^2*Li(2,z)*a1^2*a3 + 1/2*ln(1 - z)^2*Li(2,z)* a1^2*a2 + ln(1 - z)*Li(3,z)*e2^3 + ln(1 - z)*Li(3,z)*e1*e2^2 + ln(1 - z)*Li(3,z)*e1^2*e2 + ln(1 - z)*Li(3,z)*e1^3 + ln(1 - z)*Li(3,z)*c1 *e2^2 + ln(1 - z)*Li(3,z)*c1*e1*e2 + ln(1 - z)*Li(3,z)*c1*e1^2 + ln(1 - z)*Li(3,z)*c1^2*e2 + ln(1 - z)*Li(3,z)*c1^2*e1 + ln(1 - z)*Li(3,z) *c1^3 - ln(1 - z)*Li(3,z)*a4*e2^2 - ln(1 - z)*Li(3,z)*a4*e1*e2 - ln(1 - z)*Li(3,z)*a4*e1^2 - ln(1 - z)*Li(3,z)*a4*c1*e2 - ln(1 - z)*Li(3,z )*a4*c1*e1 - ln(1 - z)*Li(3,z)*a4*c1^2 - ln(1 - z)*Li(3,z)*a3*e2^2 - ln(1 - z)*Li(3,z)*a3*e1*e2 - ln(1 - z)*Li(3,z)*a3*e1^2 - ln(1 - z)* Li(3,z)*a3*c1*e2 - ln(1 - z)*Li(3,z)*a3*c1*e1 - ln(1 - z)*Li(3,z)*a3* c1^2 + ln(1 - z)*Li(3,z)*a3*a4*e2 + ln(1 - z)*Li(3,z)*a3*a4*e1 + ln(1 - z)*Li(3,z)*a3*a4*c1 - ln(1 - z)*Li(3,z)*a2*e2^2 - ln(1 - z)*Li(3,z )*a2*e1*e2 - ln(1 - z)*Li(3,z)*a2*e1^2 - ln(1 - z)*Li(3,z)*a2*c1*e2 - ln(1 - z)*Li(3,z)*a2*c1*e1 - ln(1 - z)*Li(3,z)*a2*c1^2 + ln(1 - z) *Li(3,z)*a2*a4*e2 + ln(1 - z)*Li(3,z)*a2*a4*e1 + ln(1 - z)*Li(3,z)*a2 *a4*c1 + ln(1 - z)*Li(3,z)*a2*a3*e2 + ln(1 - z)*Li(3,z)*a2*a3*e1 + ln(1 - z)*Li(3,z)*a2*a3*c1 - ln(1 - z)*Li(3,z)*a2*a3*a4 - ln(1 - z)* Li(3,z)*a1*e2^2 - ln(1 - z)*Li(3,z)*a1*e1*e2 - ln(1 - z)*Li(3,z)*a1* e1^2 - ln(1 - z)*Li(3,z)*a1*c1*e2 - ln(1 - z)*Li(3,z)*a1*c1*e1 - ln(1 - z)*Li(3,z)*a1*c1^2 + ln(1 - z)*Li(3,z)*a1*a4*e2 + ln(1 - z)*Li(3,z )*a1*a4*e1 + ln(1 - z)*Li(3,z)*a1*a4*c1 + ln(1 - z)*Li(3,z)*a1*a3*e2 + ln(1 - z)*Li(3,z)*a1*a3*e1 + ln(1 - z)*Li(3,z)*a1*a3*c1 - ln(1 - z )*Li(3,z)*a1*a3*a4 + ln(1 - z)*Li(3,z)*a1*a2*e2 + ln(1 - z)*Li(3,z)* a1*a2*e1 + ln(1 - z)*Li(3,z)*a1*a2*c1 - ln(1 - z)*Li(3,z)*a1*a2*a4 - ln(1 - z)*Li(3,z)*a1*a2*a3 + 1/2*Li(2,z)^2*e2^3 + 1/2*Li(2,z)^2*e1* e2^2 + 1/2*Li(2,z)^2*e1^2*e2 + 1/2*Li(2,z)^2*e1^3 - 1/2*Li(2,z)^2*a4* e2^2 - 1/2*Li(2,z)^2*a4*e1*e2 - 1/2*Li(2,z)^2*a4*e1^2 - 1/2*Li(2,z)^2 *a3*e2^2 - 1/2*Li(2,z)^2*a3*e1*e2 - 1/2*Li(2,z)^2*a3*e1^2 + 1/2*Li(2, z)^2*a3*a4*e2 + 1/2*Li(2,z)^2*a3*a4*e1 - 1/2*Li(2,z)^2*a2*e2^2 - 1/2* Li(2,z)^2*a2*e1*e2 - 1/2*Li(2,z)^2*a2*e1^2 + 1/2*Li(2,z)^2*a2*a4*e2 + 1/2*Li(2,z)^2*a2*a4*e1 + 1/2*Li(2,z)^2*a2*a3*e2 + 1/2*Li(2,z)^2*a2 *a3*e1 - 1/2*Li(2,z)^2*a2*a3*a4 - 1/2*Li(2,z)^2*a1*e2^2 - 1/2*Li(2,z) ^2*a1*e1*e2 - 1/2*Li(2,z)^2*a1*e1^2 + 1/2*Li(2,z)^2*a1*a4*e2 + 1/2* Li(2,z)^2*a1*a4*e1 + 1/2*Li(2,z)^2*a1*a3*e2 + 1/2*Li(2,z)^2*a1*a3*e1 - 1/2*Li(2,z)^2*a1*a3*a4 + 1/2*Li(2,z)^2*a1*a2*e2 + 1/2*Li(2,z)^2*a1 *a2*e1 - 1/2*Li(2,z)^2*a1*a2*a4 - 1/2*Li(2,z)^2*a1*a2*a3 - Li(4,z)* c1^3 ) + ep^4*FI43E(a1,a2,a3,a4,c1,e1,e2,z,ep^4) ); .sort **************************************************************************************** * * FI43F = Hypergeometric3F2[1+a1*ep,1+a2*ep,1+a3*ep,2+d1*ep; 2+c1*ep, 2+c2*ep, 1+e1*ep;z] * **************************************************************************************** id FI43F(a1?,a2?,a3?,d1?,c1?,c2?,e1?,z?,ep?) = 1/z*[1+c1*ep]*[1+c2*ep]*[1+c3*ep]/[1+d1*ep]*( - ln(1 - z) + ep * ( - 1/2*ln(1 - z)^2*e1 + 1/2*ln(1 - z)^2*d1 - 1/2*ln(1 - z)^2* c2 - 1/2*ln(1 - z)^2*c1 + 1/2*ln(1 - z)^2*a3 + 1/2*ln(1 - z)^2*a2 + 1/ 2*ln(1 - z)^2*a1 + Li(2,z)*d1 - Li(2,z)*c2 - Li(2,z)*c1 ) + ep^2 * ( - 2*S(1,2,z)*e1^2 + S(1,2,z)*d1*e1 + S(1,2,z)*d1^2 - S(1,2, z)*c2*e1 - S(1,2,z)*c2^2 - S(1,2,z)*c1*e1 - S(1,2,z)*c1^2 + 2*S(1,2,z )*a3*e1 - S(1,2,z)*a3*d1 + S(1,2,z)*a3*c2 + S(1,2,z)*a3*c1 + 2*S(1,2, z)*a2*e1 - S(1,2,z)*a2*d1 + S(1,2,z)*a2*c2 + S(1,2,z)*a2*c1 - 2*S(1,2 ,z)*a2*a3 + 2*S(1,2,z)*a1*e1 - S(1,2,z)*a1*d1 + S(1,2,z)*a1*c2 + S(1, 2,z)*a1*c1 - 2*S(1,2,z)*a1*a3 - 2*S(1,2,z)*a1*a2 - 1/6*ln(1 - z)^3* e1^2 + 1/3*ln(1 - z)^3*d1*e1 - 1/6*ln(1 - z)^3*d1^2 - 1/3*ln(1 - z)^3 *c2*e1 + 1/3*ln(1 - z)^3*c2*d1 - 1/6*ln(1 - z)^3*c2^2 - 1/3*ln(1 - z) ^3*c1*e1 + 1/3*ln(1 - z)^3*c1*d1 - 1/3*ln(1 - z)^3*c1*c2 - 1/6*ln(1 - z)^3*c1^2 + 1/3*ln(1 - z)^3*a3*e1 - 1/3*ln(1 - z)^3*a3*d1 + 1/3* ln(1 - z)^3*a3*c2 + 1/3*ln(1 - z)^3*a3*c1 - 1/6*ln(1 - z)^3*a3^2 + 1/ 3*ln(1 - z)^3*a2*e1 - 1/3*ln(1 - z)^3*a2*d1 + 1/3*ln(1 - z)^3*a2*c2 + 1/3*ln(1 - z)^3*a2*c1 - 1/3*ln(1 - z)^3*a2*a3 - 1/6*ln(1 - z)^3* a2^2 + 1/3*ln(1 - z)^3*a1*e1 - 1/3*ln(1 - z)^3*a1*d1 + 1/3*ln(1 - z)^ 3*a1*c2 + 1/3*ln(1 - z)^3*a1*c1 - 1/3*ln(1 - z)^3*a1*a3 - 1/3*ln(1 - z)^3*a1*a2 - 1/6*ln(1 - z)^3*a1^2 - ln(1 - z)*Li(2,z)*e1^2 + ln(1 - z )*Li(2,z)*d1*e1 - ln(1 - z)*Li(2,z)*c2*e1 + ln(1 - z)*Li(2,z)*c2*d1 - ln(1 - z)*Li(2,z)*c2^2 - ln(1 - z)*Li(2,z)*c1*e1 + ln(1 - z)*Li(2, z)*c1*d1 - ln(1 - z)*Li(2,z)*c1*c2 - ln(1 - z)*Li(2,z)*c1^2 + ln(1 - z)*Li(2,z)*a3*e1 - ln(1 - z)*Li(2,z)*a3*d1 + ln(1 - z)*Li(2,z)*a3*c2 + ln(1 - z)*Li(2,z)*a3*c1 + ln(1 - z)*Li(2,z)*a2*e1 - ln(1 - z)*Li(2 ,z)*a2*d1 + ln(1 - z)*Li(2,z)*a2*c2 + ln(1 - z)*Li(2,z)*a2*c1 - ln(1 - z)*Li(2,z)*a2*a3 + ln(1 - z)*Li(2,z)*a1*e1 - ln(1 - z)*Li(2,z)*a1* d1 + ln(1 - z)*Li(2,z)*a1*c2 + ln(1 - z)*Li(2,z)*a1*c1 - ln(1 - z)* Li(2,z)*a1*a3 - ln(1 - z)*Li(2,z)*a1*a2 - Li(3,z)*c2*d1 + Li(3,z)* c2^2 - Li(3,z)*c1*d1 + Li(3,z)*c1*c2 + Li(3,z)*c1^2 ) + ep^3 * ( - S(1,2,z)*ln(1 - z)*e1^3 + 2*S(1,2,z)*ln(1 - z)*d1*e1^2 - S(1,2,z)*ln(1 - z)*d1^2*e1 - 2*S(1,2,z)*ln(1 - z)*c2*e1^2 + 3*S(1,2,z )*ln(1 - z)*c2*d1*e1 - S(1,2,z)*ln(1 - z)*c2*d1^2 - 2*S(1,2,z)*ln(1 - z)*c2^2*e1 + 2*S(1,2,z)*ln(1 - z)*c2^2*d1 - S(1,2,z)*ln(1 - z)* c2^3 - 2*S(1,2,z)*ln(1 - z)*c1*e1^2 + 3*S(1,2,z)*ln(1 - z)*c1*d1*e1 - S(1,2,z)*ln(1 - z)*c1*d1^2 - 3*S(1,2,z)*ln(1 - z)*c1*c2*e1 + 3*S(1 ,2,z)*ln(1 - z)*c1*c2*d1 - 2*S(1,2,z)*ln(1 - z)*c1*c2^2 - 2*S(1,2,z)* ln(1 - z)*c1^2*e1 + 2*S(1,2,z)*ln(1 - z)*c1^2*d1 - 2*S(1,2,z)*ln(1 - z)*c1^2*c2 - S(1,2,z)*ln(1 - z)*c1^3 + 2*S(1,2,z)*ln(1 - z)*a3*e1^2 - 3*S(1,2,z)*ln(1 - z)*a3*d1*e1 + S(1,2,z)*ln(1 - z)*a3*d1^2 + 3*S(1 ,2,z)*ln(1 - z)*a3*c2*e1 - 3*S(1,2,z)*ln(1 - z)*a3*c2*d1 + 2*S(1,2,z) *ln(1 - z)*a3*c2^2 + 3*S(1,2,z)*ln(1 - z)*a3*c1*e1 - 3*S(1,2,z)*ln(1 - z)*a3*c1*d1 + 3*S(1,2,z)*ln(1 - z)*a3*c1*c2 + 2*S(1,2,z)*ln(1 - z) *a3*c1^2 - S(1,2,z)*ln(1 - z)*a3^2*e1 + S(1,2,z)*ln(1 - z)*a3^2*d1 - S(1,2,z)*ln(1 - z)*a3^2*c2 - S(1,2,z)*ln(1 - z)*a3^2*c1 + 2*S(1,2,z)* ln(1 - z)*a2*e1^2 - 3*S(1,2,z)*ln(1 - z)*a2*d1*e1 + S(1,2,z)*ln(1 - z )*a2*d1^2 + 3*S(1,2,z)*ln(1 - z)*a2*c2*e1 - 3*S(1,2,z)*ln(1 - z)*a2* c2*d1 + 2*S(1,2,z)*ln(1 - z)*a2*c2^2 + 3*S(1,2,z)*ln(1 - z)*a2*c1*e1 - 3*S(1,2,z)*ln(1 - z)*a2*c1*d1 + 3*S(1,2,z)*ln(1 - z)*a2*c1*c2 + 2* S(1,2,z)*ln(1 - z)*a2*c1^2 - 3*S(1,2,z)*ln(1 - z)*a2*a3*e1 + 3*S(1,2, z)*ln(1 - z)*a2*a3*d1 - 3*S(1,2,z)*ln(1 - z)*a2*a3*c2 - 3*S(1,2,z)* ln(1 - z)*a2*a3*c1 + S(1,2,z)*ln(1 - z)*a2*a3^2 - S(1,2,z)*ln(1 - z)* a2^2*e1 + S(1,2,z)*ln(1 - z)*a2^2*d1 - S(1,2,z)*ln(1 - z)*a2^2*c2 - S(1,2,z)*ln(1 - z)*a2^2*c1 + S(1,2,z)*ln(1 - z)*a2^2*a3 + 2*S(1,2,z)* ln(1 - z)*a1*e1^2 - 3*S(1,2,z)*ln(1 - z)*a1*d1*e1 + S(1,2,z)*ln(1 - z )*a1*d1^2 + 3*S(1,2,z)*ln(1 - z)*a1*c2*e1 - 3*S(1,2,z)*ln(1 - z)*a1* c2*d1 + 2*S(1,2,z)*ln(1 - z)*a1*c2^2 + 3*S(1,2,z)*ln(1 - z)*a1*c1*e1 - 3*S(1,2,z)*ln(1 - z)*a1*c1*d1 + 3*S(1,2,z)*ln(1 - z)*a1*c1*c2 + 2* S(1,2,z)*ln(1 - z)*a1*c1^2 - 3*S(1,2,z)*ln(1 - z)*a1*a3*e1 + 3*S(1,2, z)*ln(1 - z)*a1*a3*d1 - 3*S(1,2,z)*ln(1 - z)*a1*a3*c2 - 3*S(1,2,z)* ln(1 - z)*a1*a3*c1 + S(1,2,z)*ln(1 - z)*a1*a3^2 - 3*S(1,2,z)*ln(1 - z )*a1*a2*e1 + 3*S(1,2,z)*ln(1 - z)*a1*a2*d1 - 3*S(1,2,z)*ln(1 - z)*a1* a2*c2 - 3*S(1,2,z)*ln(1 - z)*a1*a2*c1 + 3*S(1,2,z)*ln(1 - z)*a1*a2*a3 + S(1,2,z)*ln(1 - z)*a1*a2^2 - S(1,2,z)*ln(1 - z)*a1^2*e1 + S(1,2,z) *ln(1 - z)*a1^2*d1 - S(1,2,z)*ln(1 - z)*a1^2*c2 - S(1,2,z)*ln(1 - z)* a1^2*c1 + S(1,2,z)*ln(1 - z)*a1^2*a3 + S(1,2,z)*ln(1 - z)*a1^2*a2 + S(1,3,z)*d1*e1^2 - 2*S(1,3,z)*d1^2*e1 + S(1,3,z)*d1^3 - S(1,3,z)*c2* e1^2 + 4*S(1,3,z)*c2*d1*e1 - 3*S(1,3,z)*c2*d1^2 - 2*S(1,3,z)*c2^2*e1 + 3*S(1,3,z)*c2^2*d1 - S(1,3,z)*c2^3 - S(1,3,z)*c1*e1^2 + 4*S(1,3,z) *c1*d1*e1 - 3*S(1,3,z)*c1*d1^2 - 4*S(1,3,z)*c1*c2*e1 + 6*S(1,3,z)*c1* c2*d1 - 3*S(1,3,z)*c1*c2^2 - 2*S(1,3,z)*c1^2*e1 + 3*S(1,3,z)*c1^2*d1 - 3*S(1,3,z)*c1^2*c2 - S(1,3,z)*c1^3 - 2*S(1,3,z)*a3*d1*e1 + 2*S(1,3 ,z)*a3*d1^2 + 2*S(1,3,z)*a3*c2*e1 - 4*S(1,3,z)*a3*c2*d1 + 2*S(1,3,z)* a3*c2^2 + 2*S(1,3,z)*a3*c1*e1 - 4*S(1,3,z)*a3*c1*d1 + 4*S(1,3,z)*a3* c1*c2 + 2*S(1,3,z)*a3*c1^2 + S(1,3,z)*a3^2*d1 - S(1,3,z)*a3^2*c2 - S( 1,3,z)*a3^2*c1 - 2*S(1,3,z)*a2*d1*e1 + 2*S(1,3,z)*a2*d1^2 + 2*S(1,3,z )*a2*c2*e1 - 4*S(1,3,z)*a2*c2*d1 + 2*S(1,3,z)*a2*c2^2 + 2*S(1,3,z)*a2 *c1*e1 - 4*S(1,3,z)*a2*c1*d1 + 4*S(1,3,z)*a2*c1*c2 + 2*S(1,3,z)*a2* c1^2 + 2*S(1,3,z)*a2*a3*d1 - 2*S(1,3,z)*a2*a3*c2 - 2*S(1,3,z)*a2*a3* c1 + S(1,3,z)*a2^2*d1 - S(1,3,z)*a2^2*c2 - S(1,3,z)*a2^2*c1 - 2*S(1,3 ,z)*a1*d1*e1 + 2*S(1,3,z)*a1*d1^2 + 2*S(1,3,z)*a1*c2*e1 - 4*S(1,3,z)* a1*c2*d1 + 2*S(1,3,z)*a1*c2^2 + 2*S(1,3,z)*a1*c1*e1 - 4*S(1,3,z)*a1* c1*d1 + 4*S(1,3,z)*a1*c1*c2 + 2*S(1,3,z)*a1*c1^2 + 2*S(1,3,z)*a1*a3* d1 - 2*S(1,3,z)*a1*a3*c2 - 2*S(1,3,z)*a1*a3*c1 + 2*S(1,3,z)*a1*a2*d1 - 2*S(1,3,z)*a1*a2*c2 - 2*S(1,3,z)*a1*a2*c1 + S(1,3,z)*a1^2*d1 - S(1 ,3,z)*a1^2*c2 - S(1,3,z)*a1^2*c1 - 2*S(2,2,z)*d1*e1^2 + 2*S(2,2,z)* d1^2*e1 + 2*S(2,2,z)*c2*e1^2 - 3*S(2,2,z)*c2*d1*e1 + S(2,2,z)*c2*d1^2 + S(2,2,z)*c2^2*e1 - 2*S(2,2,z)*c2^2*d1 + S(2,2,z)*c2^3 + 2*S(2,2,z) *c1*e1^2 - 3*S(2,2,z)*c1*d1*e1 + S(2,2,z)*c1*d1^2 + 3*S(2,2,z)*c1*c2* e1 - 3*S(2,2,z)*c1*c2*d1 + 2*S(2,2,z)*c1*c2^2 + S(2,2,z)*c1^2*e1 - 2* S(2,2,z)*c1^2*d1 + 2*S(2,2,z)*c1^2*c2 + S(2,2,z)*c1^3 + 2*S(2,2,z)*a3 *d1*e1 - 2*S(2,2,z)*a3*d1^2 - 2*S(2,2,z)*a3*c2*e1 + 3*S(2,2,z)*a3*c2* d1 - S(2,2,z)*a3*c2^2 - 2*S(2,2,z)*a3*c1*e1 + 3*S(2,2,z)*a3*c1*d1 - 3 *S(2,2,z)*a3*c1*c2 - S(2,2,z)*a3*c1^2 + 2*S(2,2,z)*a2*d1*e1 - 2*S(2,2 ,z)*a2*d1^2 - 2*S(2,2,z)*a2*c2*e1 + 3*S(2,2,z)*a2*c2*d1 - S(2,2,z)*a2 *c2^2 - 2*S(2,2,z)*a2*c1*e1 + 3*S(2,2,z)*a2*c1*d1 - 3*S(2,2,z)*a2*c1* c2 - S(2,2,z)*a2*c1^2 - 2*S(2,2,z)*a2*a3*d1 + 2*S(2,2,z)*a2*a3*c2 + 2 *S(2,2,z)*a2*a3*c1 + 2*S(2,2,z)*a1*d1*e1 - 2*S(2,2,z)*a1*d1^2 - 2*S(2 ,2,z)*a1*c2*e1 + 3*S(2,2,z)*a1*c2*d1 - S(2,2,z)*a1*c2^2 - 2*S(2,2,z)* a1*c1*e1 + 3*S(2,2,z)*a1*c1*d1 - 3*S(2,2,z)*a1*c1*c2 - S(2,2,z)*a1* c1^2 - 2*S(2,2,z)*a1*a3*d1 + 2*S(2,2,z)*a1*a3*c2 + 2*S(2,2,z)*a1*a3* c1 - 2*S(2,2,z)*a1*a2*d1 + 2*S(2,2,z)*a1*a2*c2 + 2*S(2,2,z)*a1*a2*c1 - 1/24*ln(1 - z)^4*e1^3 + 1/8*ln(1 - z)^4*d1*e1^2 - 1/8*ln(1 - z)^4* d1^2*e1 + 1/24*ln(1 - z)^4*d1^3 - 1/8*ln(1 - z)^4*c2*e1^2 + 1/4*ln(1 - z)^4*c2*d1*e1 - 1/8*ln(1 - z)^4*c2*d1^2 - 1/8*ln(1 - z)^4*c2^2*e1 + 1/8*ln(1 - z)^4*c2^2*d1 - 1/24*ln(1 - z)^4*c2^3 - 1/8*ln(1 - z)^4* c1*e1^2 + 1/4*ln(1 - z)^4*c1*d1*e1 - 1/8*ln(1 - z)^4*c1*d1^2 - 1/4* ln(1 - z)^4*c1*c2*e1 + 1/4*ln(1 - z)^4*c1*c2*d1 - 1/8*ln(1 - z)^4*c1* c2^2 - 1/8*ln(1 - z)^4*c1^2*e1 + 1/8*ln(1 - z)^4*c1^2*d1 - 1/8*ln(1 - z)^4*c1^2*c2 - 1/24*ln(1 - z)^4*c1^3 + 1/8*ln(1 - z)^4*a3*e1^2 - 1/ 4*ln(1 - z)^4*a3*d1*e1 + 1/8*ln(1 - z)^4*a3*d1^2 + 1/4*ln(1 - z)^4*a3 *c2*e1 - 1/4*ln(1 - z)^4*a3*c2*d1 + 1/8*ln(1 - z)^4*a3*c2^2 + 1/4*ln( 1 - z)^4*a3*c1*e1 - 1/4*ln(1 - z)^4*a3*c1*d1 + 1/4*ln(1 - z)^4*a3*c1* c2 + 1/8*ln(1 - z)^4*a3*c1^2 - 1/8*ln(1 - z)^4*a3^2*e1 + 1/8*ln(1 - z )^4*a3^2*d1 - 1/8*ln(1 - z)^4*a3^2*c2 - 1/8*ln(1 - z)^4*a3^2*c1 + 1/ 24*ln(1 - z)^4*a3^3 + 1/8*ln(1 - z)^4*a2*e1^2 - 1/4*ln(1 - z)^4*a2*d1 *e1 + 1/8*ln(1 - z)^4*a2*d1^2 + 1/4*ln(1 - z)^4*a2*c2*e1 - 1/4*ln(1 - z)^4*a2*c2*d1 + 1/8*ln(1 - z)^4*a2*c2^2 + 1/4*ln(1 - z)^4*a2*c1*e1 - 1/4*ln(1 - z)^4*a2*c1*d1 + 1/4*ln(1 - z)^4*a2*c1*c2 + 1/8*ln(1 - z )^4*a2*c1^2 - 1/4*ln(1 - z)^4*a2*a3*e1 + 1/4*ln(1 - z)^4*a2*a3*d1 - 1/ 4*ln(1 - z)^4*a2*a3*c2 - 1/4*ln(1 - z)^4*a2*a3*c1 + 1/8*ln(1 - z)^4* a2*a3^2 - 1/8*ln(1 - z)^4*a2^2*e1 + 1/8*ln(1 - z)^4*a2^2*d1 - 1/8*ln( 1 - z)^4*a2^2*c2 - 1/8*ln(1 - z)^4*a2^2*c1 + 1/8*ln(1 - z)^4*a2^2*a3 + 1/24*ln(1 - z)^4*a2^3 + 1/8*ln(1 - z)^4*a1*e1^2 - 1/4*ln(1 - z)^4* a1*d1*e1 + 1/8*ln(1 - z)^4*a1*d1^2 + 1/4*ln(1 - z)^4*a1*c2*e1 - 1/4* ln(1 - z)^4*a1*c2*d1 + 1/8*ln(1 - z)^4*a1*c2^2 + 1/4*ln(1 - z)^4*a1* c1*e1 - 1/4*ln(1 - z)^4*a1*c1*d1 + 1/4*ln(1 - z)^4*a1*c1*c2 + 1/8*ln( 1 - z)^4*a1*c1^2 - 1/4*ln(1 - z)^4*a1*a3*e1 + 1/4*ln(1 - z)^4*a1*a3* d1 - 1/4*ln(1 - z)^4*a1*a3*c2 - 1/4*ln(1 - z)^4*a1*a3*c1 + 1/8*ln(1 - z)^4*a1*a3^2 - 1/4*ln(1 - z)^4*a1*a2*e1 + 1/4*ln(1 - z)^4*a1*a2*d1 - 1/4*ln(1 - z)^4*a1*a2*c2 - 1/4*ln(1 - z)^4*a1*a2*c1 + 1/4*ln(1 - z )^4*a1*a2*a3 + 1/8*ln(1 - z)^4*a1*a2^2 - 1/8*ln(1 - z)^4*a1^2*e1 + 1/ 8*ln(1 - z)^4*a1^2*d1 - 1/8*ln(1 - z)^4*a1^2*c2 - 1/8*ln(1 - z)^4* a1^2*c1 + 1/8*ln(1 - z)^4*a1^2*a3 + 1/8*ln(1 - z)^4*a1^2*a2 + 1/24* ln(1 - z)^4*a1^3 - 1/2*ln(1 - z)^2*Li(2,z)*e1^3 + ln(1 - z)^2*Li(2,z) *d1*e1^2 - 1/2*ln(1 - z)^2*Li(2,z)*d1^2*e1 - ln(1 - z)^2*Li(2,z)*c2* e1^2 + 3/2*ln(1 - z)^2*Li(2,z)*c2*d1*e1 - 1/2*ln(1 - z)^2*Li(2,z)*c2* d1^2 - ln(1 - z)^2*Li(2,z)*c2^2*e1 + ln(1 - z)^2*Li(2,z)*c2^2*d1 - 1/ 2*ln(1 - z)^2*Li(2,z)*c2^3 - ln(1 - z)^2*Li(2,z)*c1*e1^2 + 3/2*ln(1 - z)^2*Li(2,z)*c1*d1*e1 - 1/2*ln(1 - z)^2*Li(2,z)*c1*d1^2 - 3/2*ln(1 - z)^2*Li(2,z)*c1*c2*e1 + 3/2*ln(1 - z)^2*Li(2,z)*c1*c2*d1 - ln(1 - z)^2*Li(2,z)*c1*c2^2 - ln(1 - z)^2*Li(2,z)*c1^2*e1 + ln(1 - z)^2*Li(2 ,z)*c1^2*d1 - ln(1 - z)^2*Li(2,z)*c1^2*c2 - 1/2*ln(1 - z)^2*Li(2,z)* c1^3 + ln(1 - z)^2*Li(2,z)*a3*e1^2 - 3/2*ln(1 - z)^2*Li(2,z)*a3*d1*e1 + 1/2*ln(1 - z)^2*Li(2,z)*a3*d1^2 + 3/2*ln(1 - z)^2*Li(2,z)*a3*c2*e1 - 3/2*ln(1 - z)^2*Li(2,z)*a3*c2*d1 + ln(1 - z)^2*Li(2,z)*a3*c2^2 + 3/ 2*ln(1 - z)^2*Li(2,z)*a3*c1*e1 - 3/2*ln(1 - z)^2*Li(2,z)*a3*c1*d1 + 3/ 2*ln(1 - z)^2*Li(2,z)*a3*c1*c2 + ln(1 - z)^2*Li(2,z)*a3*c1^2 - 1/2* ln(1 - z)^2*Li(2,z)*a3^2*e1 + 1/2*ln(1 - z)^2*Li(2,z)*a3^2*d1 - 1/2* ln(1 - z)^2*Li(2,z)*a3^2*c2 - 1/2*ln(1 - z)^2*Li(2,z)*a3^2*c1 + ln(1 - z)^2*Li(2,z)*a2*e1^2 - 3/2*ln(1 - z)^2*Li(2,z)*a2*d1*e1 + 1/2*ln(1 - z)^2*Li(2,z)*a2*d1^2 + 3/2*ln(1 - z)^2*Li(2,z)*a2*c2*e1 - 3/2*ln(1 - z)^2*Li(2,z)*a2*c2*d1 + ln(1 - z)^2*Li(2,z)*a2*c2^2 + 3/2*ln(1 - z )^2*Li(2,z)*a2*c1*e1 - 3/2*ln(1 - z)^2*Li(2,z)*a2*c1*d1 + 3/2*ln(1 - z)^2*Li(2,z)*a2*c1*c2 + ln(1 - z)^2*Li(2,z)*a2*c1^2 - 3/2*ln(1 - z)^2 *Li(2,z)*a2*a3*e1 + 3/2*ln(1 - z)^2*Li(2,z)*a2*a3*d1 - 3/2*ln(1 - z)^ 2*Li(2,z)*a2*a3*c2 - 3/2*ln(1 - z)^2*Li(2,z)*a2*a3*c1 + 1/2*ln(1 - z) ^2*Li(2,z)*a2*a3^2 - 1/2*ln(1 - z)^2*Li(2,z)*a2^2*e1 + 1/2*ln(1 - z)^ 2*Li(2,z)*a2^2*d1 - 1/2*ln(1 - z)^2*Li(2,z)*a2^2*c2 - 1/2*ln(1 - z)^2 *Li(2,z)*a2^2*c1 + 1/2*ln(1 - z)^2*Li(2,z)*a2^2*a3 + ln(1 - z)^2*Li(2 ,z)*a1*e1^2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*d1*e1 + 1/2*ln(1 - z)^2*Li(2 ,z)*a1*d1^2 + 3/2*ln(1 - z)^2*Li(2,z)*a1*c2*e1 - 3/2*ln(1 - z)^2*Li(2 ,z)*a1*c2*d1 + ln(1 - z)^2*Li(2,z)*a1*c2^2 + 3/2*ln(1 - z)^2*Li(2,z)* a1*c1*e1 - 3/2*ln(1 - z)^2*Li(2,z)*a1*c1*d1 + 3/2*ln(1 - z)^2*Li(2,z) *a1*c1*c2 + ln(1 - z)^2*Li(2,z)*a1*c1^2 - 3/2*ln(1 - z)^2*Li(2,z)*a1* a3*e1 + 3/2*ln(1 - z)^2*Li(2,z)*a1*a3*d1 - 3/2*ln(1 - z)^2*Li(2,z)*a1 *a3*c2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a3*c1 + 1/2*ln(1 - z)^2*Li(2,z)* a1*a3^2 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a2*e1 + 3/2*ln(1 - z)^2*Li(2,z)* a1*a2*d1 - 3/2*ln(1 - z)^2*Li(2,z)*a1*a2*c2 - 3/2*ln(1 - z)^2*Li(2,z) *a1*a2*c1 + 3/2*ln(1 - z)^2*Li(2,z)*a1*a2*a3 + 1/2*ln(1 - z)^2*Li(2,z )*a1*a2^2 - 1/2*ln(1 - z)^2*Li(2,z)*a1^2*e1 + 1/2*ln(1 - z)^2*Li(2,z) *a1^2*d1 - 1/2*ln(1 - z)^2*Li(2,z)*a1^2*c2 - 1/2*ln(1 - z)^2*Li(2,z)* a1^2*c1 + 1/2*ln(1 - z)^2*Li(2,z)*a1^2*a3 + 1/2*ln(1 - z)^2*Li(2,z)* a1^2*a2 + ln(1 - z)*Li(3,z)*e1^3 - ln(1 - z)*Li(3,z)*d1*e1^2 + ln(1 - z)*Li(3,z)*c2*e1^2 - ln(1 - z)*Li(3,z)*c2*d1*e1 + ln(1 - z)*Li(3,z )*c2^2*e1 - ln(1 - z)*Li(3,z)*c2^2*d1 + ln(1 - z)*Li(3,z)*c2^3 + ln(1 - z)*Li(3,z)*c1*e1^2 - ln(1 - z)*Li(3,z)*c1*d1*e1 + ln(1 - z)*Li(3,z )*c1*c2*e1 - ln(1 - z)*Li(3,z)*c1*c2*d1 + ln(1 - z)*Li(3,z)*c1*c2^2 + ln(1 - z)*Li(3,z)*c1^2*e1 - ln(1 - z)*Li(3,z)*c1^2*d1 + ln(1 - z)* Li(3,z)*c1^2*c2 + ln(1 - z)*Li(3,z)*c1^3 - ln(1 - z)*Li(3,z)*a3*e1^2 + ln(1 - z)*Li(3,z)*a3*d1*e1 - ln(1 - z)*Li(3,z)*a3*c2*e1 + ln(1 - z )*Li(3,z)*a3*c2*d1 - ln(1 - z)*Li(3,z)*a3*c2^2 - ln(1 - z)*Li(3,z)*a3 *c1*e1 + ln(1 - z)*Li(3,z)*a3*c1*d1 - ln(1 - z)*Li(3,z)*a3*c1*c2 - ln(1 - z)*Li(3,z)*a3*c1^2 - ln(1 - z)*Li(3,z)*a2*e1^2 + ln(1 - z)*Li( 3,z)*a2*d1*e1 - ln(1 - z)*Li(3,z)*a2*c2*e1 + ln(1 - z)*Li(3,z)*a2*c2* d1 - ln(1 - z)*Li(3,z)*a2*c2^2 - ln(1 - z)*Li(3,z)*a2*c1*e1 + ln(1 - z)*Li(3,z)*a2*c1*d1 - ln(1 - z)*Li(3,z)*a2*c1*c2 - ln(1 - z)*Li(3,z)* a2*c1^2 + ln(1 - z)*Li(3,z)*a2*a3*e1 - ln(1 - z)*Li(3,z)*a2*a3*d1 + ln(1 - z)*Li(3,z)*a2*a3*c2 + ln(1 - z)*Li(3,z)*a2*a3*c1 - ln(1 - z)* Li(3,z)*a1*e1^2 + ln(1 - z)*Li(3,z)*a1*d1*e1 - ln(1 - z)*Li(3,z)*a1* c2*e1 + ln(1 - z)*Li(3,z)*a1*c2*d1 - ln(1 - z)*Li(3,z)*a1*c2^2 - ln(1 - z)*Li(3,z)*a1*c1*e1 + ln(1 - z)*Li(3,z)*a1*c1*d1 - ln(1 - z)*Li(3, z)*a1*c1*c2 - ln(1 - z)*Li(3,z)*a1*c1^2 + ln(1 - z)*Li(3,z)*a1*a3*e1 - ln(1 - z)*Li(3,z)*a1*a3*d1 + ln(1 - z)*Li(3,z)*a1*a3*c2 + ln(1 - z )*Li(3,z)*a1*a3*c1 + ln(1 - z)*Li(3,z)*a1*a2*e1 - ln(1 - z)*Li(3,z)* a1*a2*d1 + ln(1 - z)*Li(3,z)*a1*a2*c2 + ln(1 - z)*Li(3,z)*a1*a2*c1 - ln(1 - z)*Li(3,z)*a1*a2*a3 + 1/2*Li(2,z)^2*e1^3 - 1/2*Li(2,z)^2*d1^2* e1 + 1/2*Li(2,z)^2*c2*d1*e1 - 1/2*Li(2,z)^2*c2*d1^2 + 1/2*Li(2,z)^2* c2^2*d1 + 1/2*Li(2,z)^2*c1*d1*e1 - 1/2*Li(2,z)^2*c1*d1^2 - 1/2*Li(2,z )^2*c1*c2*e1 + Li(2,z)^2*c1*c2*d1 - 1/2*Li(2,z)^2*c1*c2^2 + 1/2*Li(2, z)^2*c1^2*d1 - 1/2*Li(2,z)^2*c1^2*c2 - 1/2*Li(2,z)^2*a3*e1^2 + 1/2* Li(2,z)^2*a3*d1^2 - 1/2*Li(2,z)^2*a3*c2*d1 - 1/2*Li(2,z)^2*a3*c1*d1 + 1/2*Li(2,z)^2*a3*c1*c2 - 1/2*Li(2,z)^2*a2*e1^2 + 1/2*Li(2,z)^2*a2* d1^2 - 1/2*Li(2,z)^2*a2*c2*d1 - 1/2*Li(2,z)^2*a2*c1*d1 + 1/2*Li(2,z)^ 2*a2*c1*c2 + 1/2*Li(2,z)^2*a2*a3*e1 - 1/2*Li(2,z)^2*a1*e1^2 + 1/2*Li( 2,z)^2*a1*d1^2 - 1/2*Li(2,z)^2*a1*c2*d1 - 1/2*Li(2,z)^2*a1*c1*d1 + 1/ 2*Li(2,z)^2*a1*c1*c2 + 1/2*Li(2,z)^2*a1*a3*e1 + 1/2*Li(2,z)^2*a1*a2* e1 - 1/2*Li(2,z)^2*a1*a2*a3 + Li(4,z)*c2^2*d1 - Li(4,z)*c2^3 + Li(4,z )*c1*c2*d1 - Li(4,z)*c1*c2^2 + Li(4,z)*c1^2*d1 - Li(4,z)*c1^2*c2 - Li(4,z)*c1^3 ) + ep^4*FI43F(a1,a2,a3,d1,c1,c2,e1,z,ep^4) ); .sort b ep,z,[1+c1*ep],[1+c2*ep],[1+c3*ep],[1+d1*ep],[1+d2*ep]; print; .end