Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0859)

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=1/2

http://functions.wolfram.com/07.22.03.0859.01

Input Form

HypergeometricPFQ[{-(9/2)}, {1/2, 9/2}, z] == (1/(2359296 z^(7/2))) (2 Sqrt[z] (127575 - 51030 z + 85050 z^2 + 633924 z^3 - 403830 z^4 + 41772 z^5 - 1148 z^6 + 8 z^7) Cosh[2 Sqrt[z]] + (-127575 - 119070 z + 28350 z^2 + 396900 z^3 - 367866 z^4 + 40668 z^5 - 1140 z^6 + 8 z^7) Sinh[2 Sqrt[z]] - 32 z^4 (99225 - 52920 z + 5292 z^2 - 144 z^3 + 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]