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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] > Series representations > Generalized power series > Expansions at z==infinity for p==q+1 > Case of simple poles





http://functions.wolfram.com/07.31.06.0018.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, q + 1]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] == (Product[Gamma[Subscript[b, k]], {k, 1, q}]/Product[Gamma[Subscript[a, k]], {k, 1, q + 1}]) Sum[GammaResidue[{{0}, {1 - Subscript[a, 1], \[Ellipsis], 1 - Subscript[a, q + 1]}}, {{}, {1 - Subscript[b, 1], \[Ellipsis], 1 - Subscript[b, q]}}, {1 - Subscript[a, k], 1, i}, -z], {k, 1, q + 1}, {i, 0, Infinity}] /; Abs[z] > 1 && ForAll[{j, k}, Element[{j, k}, Integers] && j != k && 1 <= j <= q + 1 && 1 <= k <= q + 1, !Element[Subscript[a, j] - Subscript[a, k], Integers]]










Standard Form





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MathML Form







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





2001-10-29