Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0966)

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/07.22.03.0966.01

Input Form

HypergeometricPFQ[{-(9/2)}, {7/2, 11/2}, -z] == (1/(1056964608 z^(9/2))) (2 Sqrt[z] (31255875 + 59535000 z - 104220270 z^2 + 113059800 z^3 + 94985226 z^4 + 10929312 z^5 + 378780 z^6 + 4528 z^7 + 16 z^8) Cos[2 Sqrt[z]] + (-31255875 - 17860500 z - 62477730 z^2 + 59149440 z^3 + 85872150 z^4 + 10574424 z^5 + 374340 z^6 + 4512 z^7 + 16 z^8) Sin[2 Sqrt[z]] + 32 z^2 (8037225 - 12502350 z + 18753525 z^2 + 12502350 z^3 + 1389150 z^4 + 47628 z^5 + 567 z^6 + 2 z^7) SinIntegral[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]