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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2,a3,a4},{b1,b2,b3},z] > Series representations > Residue representations





http://functions.wolfram.com/07.28.06.0025.01









  


  








Input Form





HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] == (Product[Gamma[Subscript[b, k]], {k, 1, 3}]/ Product[Gamma[Subscript[a, k]], {k, 1, 4}]) Sum[Residue[(Gamma[s] Product[Gamma[Subscript[a, k] - s], {k, 1, 4}])/ Product[Gamma[Subscript[b, k] - s], {k, 1, 3}]/(-z)^s, {s, -j}], {j, 0, Infinity}] /; Abs[z] < 1








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