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

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{-(5/4)}, {11/2, -(19/4)}, -z] == -((1/(32149216 Sqrt[2] z^(13/4))) ((4 z (36974963025 - 1649676600 z + 53300352 z^2 - 16613376 z^3 + 524288 z^4) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (61624938375 - 8227233300 z + 172747200 z^2 - 8536064 z^3 + 262144 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (924374075625 - 205575084000 z + 10751738400 z^2 + 191270400 z^3 - 68026368 z^4 + 2097152 z^5) 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]