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

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=3/4, b_1`>=-11/2

For fixed z and a₁=3/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{3/4}, {-(11/2), 17/4}, -z] == (1/(121110528 Sqrt[2] z^(11/4))) (13 (2 Sqrt[z] (-26615181285 - 27037644480 z + 4022844672 z^2 - 130744320 z^3 + 524288 z^4) BesselJ[1/4, Sqrt[z]]^2 + (133075906425 + 229819978080 z - 66285838080 z^2 + 3996647424 z^3 - 49283072 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 2 Sqrt[z] (133075906425 - 54075288960 z + 5814547200 z^2 - 149618688 z^3 + 524288 z^4) 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]