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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=1/2

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

Input Form

HypergeometricPFQ[{23/4}, {1/2, -(23/4)}, -z] == (1/(99687686175 z^(1/4))) (Sqrt[2] ((99687686175 + 398750744700 z + 559650168000 z^2 + 204518135808 z^3 - 1860009984 z^4 - 3881041920 z^5 + 432013312 z^6) BesselJ[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (99687686175 + 265833829800 z + 40315605120 z^2 - 64674312192 z^3 - 13773570048 z^4 - 1467482112 z^5 + 8388608 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 4 z (-99687686175 + 41548021200 z + 91330767360 z^2 + 9726861312 z^3 + 54853632 z^4 + 101711872 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]