Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9573)

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`=7/2

http://functions.wolfram.com/07.22.03.9573.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, 19/4}, -z] == ((2 Sqrt[z] (767555262849375 + 8612568144180000 z - 17944060239705600 z^2 + 82476868690944000 z^3 + 35867518068326400 z^4 + 3473524591165440 z^5 + 110693219041280 z^6 + 1257888546816 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]]^2 - (2302665788548125 + 22328880373800000 z - 36211944242073600 z^2 + 64787994541670400 z^3 + 33868532249395200 z^4 + 3406404224286720 z^5 + 109914252902400 z^6 + 1255204192256 z^7 + 4294967296 z^8) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (-2302665788548125 + 17361969427202400 z - 29259119540851200 z^2 + 74685102183014400 z^3 + 35040140977766400 z^4 + 3446334742855680 z^5 + 110380424626176 z^6 + 1256814804992 z^7 + 4294967296 z^8) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (105262948417536000 Sqrt[2] z^(13/4))

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]