Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.6602)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=2, b₁>=-23/4

For fixed z and a₁=2, b₁=-15/4

http://functions.wolfram.com/07.22.03.6602.01

Input Form

HypergeometricPFQ[{2}, {-(15/4), 23/4}, z] == (1/(16384 z^(19/4))) ((19 (16 E^(2 Sqrt[z]) z^(3/4) (172297125 + 34362900 z + 2648880 z^2 + 63360 z^3 + 256 z^4) + E^(4 Sqrt[z]) Sqrt[2 Pi] (516891375 - 1033782750 Sqrt[z] + 989188200 z - 599999400 z^(3/2) + 257297040 z^2 - 82162080 z^(5/2) + 19958400 z^3 - 3674880 z^(7/2) + 495360 z^4 - 44544 z^(9/2) + 2048 z^5) Erf[Sqrt[2] z^(1/4)] - Sqrt[2 Pi] (516891375 + 1033782750 Sqrt[z] + 989188200 z + 599999400 z^(3/2) + 257297040 z^2 + 82162080 z^(5/2) + 19958400 z^3 + 3674880 z^(7/2) + 495360 z^4 + 44544 z^(9/2) + 2048 z^5) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z]))

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)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]