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

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=5/2

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

Input Form

HypergeometricPFQ[{15/4}, {5/2, -(15/4)}, -z] == (1/(266805 z^(1/4))) (Sqrt[2] ((266805 + 807408 z + 237312 z^2 - 28672 z^3) BesselJ[1/4, Sqrt[z]]^2 + 8 Sqrt[z] (-237825 - 20304 z + 51456 z^2 + 4096 z^3) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (1044225 - 245520 z - 546048 z^2 + 4096 z^3) 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]