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variants of this functions
MeijerG






Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Specific values > Specialized values > Cases with m==3 > Case {m,n,p,q}={3,3,3,3}





http://functions.wolfram.com/07.34.03.1052.01









  


  










Input Form





MeijerG[{{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {}}, {{Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, {}}, z] == Pi^2 (Csc[Pi (-Subscript[b, 1] + Subscript[b, 2])] Csc[Pi (-Subscript[b, 1] + Subscript[b, 3])] Gamma[1 - Subscript[a, 1] + Subscript[b, 1]] Gamma[1 - Subscript[a, 2] + Subscript[b, 1]] Gamma[1 - Subscript[a, 3] + Subscript[b, 1]] z^Subscript[b, 1] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 1], 1 - Subscript[a, 2] + Subscript[b, 1], 1 - Subscript[a, 3] + Subscript[b, 1]}, {1 + Subscript[b, 1] - Subscript[b, 2], 1 + Subscript[b, 1] - Subscript[b, 3]}, -z] + Csc[Pi (Subscript[b, 1] - Subscript[b, 2])] Csc[Pi (-Subscript[b, 2] + Subscript[b, 3])] Gamma[1 - Subscript[a, 1] + Subscript[b, 2]] Gamma[1 - Subscript[a, 2] + Subscript[b, 2]] Gamma[1 - Subscript[a, 3] + Subscript[b, 2]] z^Subscript[b, 2] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 2], 1 - Subscript[a, 2] + Subscript[b, 2], 1 - Subscript[a, 3] + Subscript[b, 2]}, {1 - Subscript[b, 1] + Subscript[b, 2], 1 + Subscript[b, 2] - Subscript[b, 3]}, -z] + Csc[Pi (Subscript[b, 1] - Subscript[b, 3])] Csc[Pi (Subscript[b, 2] - Subscript[b, 3])] Gamma[1 - Subscript[a, 1] + Subscript[b, 3]] Gamma[1 - Subscript[a, 2] + Subscript[b, 3]] Gamma[1 - Subscript[a, 3] + Subscript[b, 3]] z^Subscript[b, 3] HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 3], 1 - Subscript[a, 2] + Subscript[b, 3], 1 - Subscript[a, 3] + Subscript[b, 3]}, {1 - Subscript[b, 1] + Subscript[b, 3], 1 - Subscript[b, 2] + Subscript[b, 3]}, -z]) /; !Element[Subscript[b, 2] - Subscript[b, 1], Integers] && !Element[Subscript[b, 3] - Subscript[b, 1], Integers] && !Element[Subscript[b, 3] - Subscript[b, 2], Integers]










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2001-10-29