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

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-7/2

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

Input Form

HypergeometricPFQ[{9/4}, {-(7/2), 19/4}, -z] == -((1/(5242880 Sqrt[2] z^(13/4))) (33 (2 Sqrt[z] (3886257375 - 4149054000 z + 641571840 z^2 - 30801920 z^3 + 262144 z^4) BesselJ[-(1/4), Sqrt[z]]^2 + (-11658772125 + 30212910000 z - 8340433920 z^2 + 687964160 z^3 - 15990784 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 2 Sqrt[z] (11658772125 - 5340862800 z + 736619520 z^2 - 32866304 z^3 + 262144 z^4) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]