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variants of this functions
HypergeometricPFQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQ[{a1,...,ap},{b1,...,bq},z] > Series representations > Asymptotic series expansions > Expansions for q>=p+2





http://functions.wolfram.com/07.31.06.0032.01









  


  








Input Form





HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, z] \[Proportional] Product[Gamma[Subscript[b, j]] (AsymptoticHypergeometricPFQRegularizedSeries[Power][ {Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, {z, Infinity, Infinity}] + AsymptoticHypergeometricPFQRegularizedSeries[ Exp][{Subscript[a, 1], \[Ellipsis], Subscript[a, p]}, {Subscript[b, 1], \[Ellipsis], Subscript[b, q]}, {z, Infinity, Infinity}]), {j, 1, q}] /; q - p >= 2 && (Abs[z] -> Infinity) && ForAll[{j, k}, Element[{j, k}, Integers] && j != k && 1 <= j <= p && 1 <= k <= p, !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