Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0463)

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=-3/2

http://functions.wolfram.com/07.22.03.0463.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(3/2), 7/2}, z] == (1/(1548288 z^(5/2))) (-2 Sqrt[z] (280665 - 187110 z - 113022 z^2 - 77148 z^3 - 217710 z^4 + 32748 z^5 - 1052 z^6 + 8 z^7) Cosh[2 Sqrt[z]] + (280665 + 187110 z + 311850 z^2 + 171612 z^3 + 190242 z^4 - 31740 z^5 + 1044 z^6 - 8 z^7) Sinh[2 Sqrt[z]] + 32 z^5 (-29106 + 4158 z - 132 z^2 + z^3) 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]