Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9501)

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`=5/2

http://functions.wolfram.com/07.22.03.9501.01

Input Form

HypergeometricPFQ[{-(19/4)}, {5/2, -(5/4)}, -z] == (1/(522112500 Sqrt[2] z^(3/4))) ((32 z (19484325 - 43936200 z + 75110400 z^2 + 36283520 z^3 + 2437120 z^4 + 32768 z^5) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (76039425 - 212688000 z + 224582400 z^2 + 139261440 z^3 + 9666560 z^4 + 131072 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (228118275 + 884822400 z - 1677312000 z^2 + 2141798400 z^3 + 1141985280 z^4 + 77725696 z^5 + 1048576 z^6) 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]