I am trying to validate https://functions.wolfram.com/07.34.16.0003.01. Mathematica result: -0.0235122-4.06565*10^-16 I and Manual result: 0.366... Please help me to match both values.
Q[{{{}, {}}, {{}, {}}}, {{{0}, {}}, {{0}, {}}}, {{{1,
1}, {}}, {{1}, {0}}}, {2, 2}] // N
(*Extended Generalized Bivariate Meijer G-Function (EGBMGF)*)
Clear All;
(*Exception*)
Q::InconsistentCoeffs = " Inconsistent coefficients ";
Q[{cst_, dst_}, {cs_, ds_}, {ct_, dt_}, {zs_, zt_}] := Module[{},
(*Only's' is used as argument in the Gamma product terms along \
with other parameters*)
Eas =
Function[v,
Product[Gamma[1 - cs[[1, n]] + v], {n, 1, Length[cs[[1]]]}]];
Fas =
Function[v,
Product[Gamma[cs[[2, n]] - v], {n, 1, Length[cs[[2]]]}]];
Ebs =
Function[v,
Product[Gamma[ds[[1, n]] - v], {n, 1, Length[ds[[1]]]}]];
Fbs =
Function[v,
Product[Gamma[1 - ds[[2, n]] + v], {n, 1, Length[ds[[2]]]}]];
Ps = Function[v, Eas[v] Ebs[v]/(Fas[v] Fbs[v])];
(*Only't' is used as argument in the Gamma product terms along \
with other parameters*)
Eat =
Function[v,
Product[Gamma[1 - ct[[1, n]] + v], {n, 1, Length[ct[[1]]]}]];
Fat =
Function[v,
Product[Gamma[ct[[2, n]] - v], {n, 1, Length[ct[[2]]]}]];
Ebt =
Function[v,
Product[Gamma[dt[[1, n]] - v], {n, 1, Length[dt[[1]]]}]];
Fbt =
Function[v,
Product[Gamma[1 - dt[[2, n]] + v], {n, 1, Length[dt[[2]]]}]];
Pt = Function[v, Eat[v] Ebt[v]/(Fat[v] Fbt[v])];
(*'s+t' is used as argument in the Gamma product terms along with \
other parameters*)
East =
Function[v,
Product[Gamma[cst[[1, n]] + v], {n, 1, Length[cst[[1]]]}]];
Fast =
Function[v,
Product[Gamma[1 - cst[[2, n]] - v], {n, 1, Length[cst[[2]]]}]];
Fbst =
Function[v,
Product[Gamma[dst[[2, n]] + v], {n, 1, Length[dst[[2]]]}]];
Pst = Function[v, East[v]/(Fast[v] Fbst[v])];
MT = Function[{v, w}, Ps[v] + Pt[w]/Pst[v + w]];
(*Countour limiters (The Gamma arguments in the numerator \
determine the value of the limiters which must be half of the least \
valued Gamma arguments)*)
As = 1/4;
At = 1/4;
Zs = zs;
Zt = zt;
W = 50;
(*The final value is calculated*)
Print[" Numerical Integration :"];
value =
1/((2 \[Pi] I)^2) NIntegrate[
MT[s, t] Zs^s Zt^t, {s, As - I W, As + I W}, {t, At - I W,
At + I W}];
(*The value is returned*)
Return[value];
];
(*End of EGBMGF*)
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