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

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`=11/2

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

Input Form

HypergeometricPFQ[{19/4}, {11/2, -(11/4)}, -z] == (1/(27104 Sqrt[2] z^(13/4))) ((-4 z (635933025 - 147583800 z + 14915712 z^2 - 952320 z^3 + 32768 z^4) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (3179665125 - 1020555900 z + 130576320 z^2 - 9556992 z^3 + 475136 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-15898325625 + 6515964000 z - 1058148000 z^2 + 92567040 z^3 - 5332992 z^4 + 131072 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]