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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=1/2

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

Input Form

HypergeometricPFQ[{19/4}, {1/2, 21/4}, -z] == -((1/(1261568 Sqrt[2] z^(15/4))) (221 (6 Sqrt[z] (135135 + 114576 z - 41216 z^2 + 4096 z^3) BesselJ[1/4, Sqrt[z]]^2 + (-2027025 - 3160080 z + 1564416 z^2 - 282624 z^3 + 65536 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 18 Sqrt[z] (225225 - 129360 z + 28928 z^2 - 4096 z^3) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2))

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]