Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.actx)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.actx.01

Input Form

HypergeometricPFQ[{7/4}, {-(11/2), 21/4}, -z] == (221 (2 Sqrt[z] (13493896911495 + 13059182283840 z - 2703764448000 z^2 + 159116525568 z^3 - 2906652672 z^4 + 8388608 z^5) BesselJ[1/4, Sqrt[z]]^2 - 3 (22489828185825 + 37758070516320 z - 13086219928320 z^2 + 1190819266560 z^3 - 36780900352 z^4 + 301989888 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (67469484557475 - 30660688840320 z + 4217872538880 z^2 - 202980556800 z^3 + 3252682752 z^4 - 8388608 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(5813305344 Sqrt[2] z^(15/4))

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]