Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0615)

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=-11/2, b_1`>=-11/2

For fixed z and a₁=-11/2, b₁=7/2

http://functions.wolfram.com/07.22.03.0615.01

Input Form

HypergeometricPFQ[{-(11/2)}, {7/2, 7/2}, z] == (1/(7398752256 z^(5/2))) (-2 Sqrt[z] (161195265 + 443263590 z - 892572282 z^2 + 197657532 z^3 - 12888390 z^4 + 309068 z^5 - 2812 z^6 + 8 z^7) Cosh[2 Sqrt[z]] + (4022865 - 110207790 z + 749375550 z^2 - 186300828 z^3 + 12594282 z^4 - 306300 z^5 + 2804 z^6 - 8 z^7) Sinh[2 Sqrt[z]] + 16 (9823275 + 52390800 z + 183367800 z^2 - 244490400 z^3 + 50935500 z^4 - 3259872 z^5 + 77616 z^6 - 704 z^7 + 2 z^8) SinhIntegral[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]