Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0477)

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/07.22.03.0477.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(1/2), 1/2}, z] == (1/11520) (2 (5760 + 75870 z - 77835 z^2 + 11666 z^3 - 438 z^4 + 4 z^5) Cosh[2 Sqrt[z]] + Sqrt[z] (39330 - 68325 z + 11250 z^2 - 434 z^3 + 4 z^4) Sinh[2 Sqrt[z]] - 8 z^(3/2) (51975 - 41580 z + 5940 z^2 - 220 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]