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variants of this functions
HypergeometricPFQ






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1},{b1,b2},z] > Series representations > Asymptotic series expansions > Expansions for any z in exponential form





http://functions.wolfram.com/07.22.06.0010.01









  


  










Input Form





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










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