Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0590)

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=5/2

http://functions.wolfram.com/07.22.03.0590.01

Input Form

HypergeometricPFQ[{-(11/2)}, {5/2, 7/2}, -z] == (1/(2312110080 z^(5/2))) (2 Sqrt[z] (-9823275 + 89999910 z + 325764810 z^2 + 98118972 z^3 + 8036862 z^4 + 231628 z^5 + 2460 z^6 + 8 z^7) Cos[2 Sqrt[z]] + (9823275 + 1683990 z + 259895790 z^2 + 91210140 z^3 + 7818258 z^4 + 229212 z^5 + 2452 z^6 + 8 z^7) Sin[2 Sqrt[z]] + 32 z (-3274425 + 22920975 z + 45841950 z^2 + 12733875 z^3 + 1018710 z^4 + 29106 z^5 + 308 z^6 + 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]