Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.5185)

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=5, b_1`>=-11/2

For fixed z and a₁=5, b₁=-11/2

http://functions.wolfram.com/07.22.03.5185.01

Input Form

HypergeometricPFQ[{5}, {-(11/2), -(11/2)}, -z] == (1/324168075) (32 Pi z^3 (16 z^(11/2) StruveH[-18, 2 Sqrt[z]] + 7 (272 z^5 StruveH[-17, 2 Sqrt[z]] + 3 (4456 z^(9/2) StruveH[-16, 2 Sqrt[z]] + 118192 z^4 StruveH[-15, 2 Sqrt[z]] + 1856621 z^(7/2) StruveH[-14, 2 Sqrt[z]] + 17851869 z^3 StruveH[-13, 2 Sqrt[z]] + 105019530 z^(5/2) StruveH[-12, 2 Sqrt[z]] + 367475070 z^2 StruveH[-11, 2 Sqrt[z]] + 719502840 z^(3/2) StruveH[-10, 2 Sqrt[z]] + 703788120 z StruveH[-9, 2 Sqrt[z]] + 275118480 Sqrt[z] StruveH[-8, 2 Sqrt[z]] + 24418800 StruveH[-7, 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]