Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.5907)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=6, b_1`>=-11/2

For fixed z and a₁=6, b₁=-9/2

http://functions.wolfram.com/07.22.03.5907.01

Input Form

HypergeometricPFQ[{6}, {-(9/2), -(7/2)}, -z] == -((1/1488375) (2 Pi z^(5/2) (32 z^5 StruveH[-16, 2 Sqrt[z]] + 5 (688 z^(9/2) StruveH[-15, 2 Sqrt[z]] + 30224 z^4 StruveH[-14, 2 Sqrt[z]] + 707304 z^(7/2) StruveH[-13, 2 Sqrt[z]] + 9643170 z^3 StruveH[-12, 2 Sqrt[z]] + 78771903 z^(5/2) StruveH[-11, 2 Sqrt[z]] + 382415670 z^2 StruveH[-10, 2 Sqrt[z]] + 1059033780 z^(3/2) StruveH[-9, 2 Sqrt[z]] + 1536756480 z StruveH[-8, 2 Sqrt[z]] + 988961400 Sqrt[z] StruveH[-7, 2 Sqrt[z]] + 190466640 StruveH[-6, 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]