Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0481)

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=-1/2

http://functions.wolfram.com/07.22.03.0481.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(1/2), 3/2}, z] == (1/(138240 Sqrt[z])) (2 Sqrt[z] (37935 + 250110 z - 158157 z^2 + 17562 z^3 - 526 z^4 + 4 z^5) Cosh[2 Sqrt[z]] + (31185 + 160110 z - 143235 z^2 + 17058 z^3 - 522 z^4 + 4 z^5) Sinh[2 Sqrt[z]] - 8 z^2 (155925 - 83160 z + 8910 z^2 - 264 z^3 + 2 z^4) 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]