Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0957)

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=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=7/2

http://functions.wolfram.com/07.22.03.0957.01

Input Form

HypergeometricPFQ[{-(9/2)}, {7/2, 7/2}, z] == (1/(231211008 z^(5/2))) (2 Sqrt[z] (-6880545 - 16057440 z + 25763976 z^2 - 4524480 z^3 + 220524 z^4 - 3520 z^5 + 16 z^6) Cosh[2 Sqrt[z]] + (-263655 - 4932900 z + 22249080 z^2 - 4322304 z^3 + 217092 z^4 - 3504 z^5 + 16 z^6) Sinh[2 Sqrt[z]] - 8 (-893025 - 4167450 z - 12502350 z^2 + 13891500 z^3 - 2315250 z^4 + 111132 z^5 - 1764 z^6 + 8 z^7) 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]