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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,a2},{b1,b2},z] > Series representations > Asymptotic series expansions > Case of simple poles





http://functions.wolfram.com/07.25.06.0009.01









  


  










Input Form





HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2]}, {Subscript[b, 1], Subscript[b, 2]}, z] \[Proportional] ((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]])/(Gamma[Subscript[a, 1]] Gamma[Subscript[a, 2]])) z^(Subscript[a, 1] + Subscript[a, 2] - Subscript[b, 1] - Subscript[b, 2]) E^z (1 + O[1/z]) + (((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[a, 2] - Subscript[a, 1]])/(Gamma[Subscript[a, 2]] Gamma[Subscript[b, 1] - Subscript[a, 1]] Gamma[Subscript[b, 2] - Subscript[a, 1]])) (1 + O[1/z]))/ (-z)^Subscript[a, 1] + (((Gamma[Subscript[b, 1]] Gamma[Subscript[b, 2]] Gamma[Subscript[a, 1] - Subscript[a, 2]])/(Gamma[Subscript[a, 1]] Gamma[Subscript[b, 1] - Subscript[a, 2]] Gamma[Subscript[b, 2] - Subscript[a, 2]])) (1 + O[1/z]))/ (-z)^Subscript[a, 2] /; (Abs[z] -> Infinity) && Subscript[a, 1] != Subscript[a, 2]










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





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