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

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`=-11/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(11/2), 9/4}, -z] == -((1/(30735936 Sqrt[2] z^(3/4))) ((6 Sqrt[z] (-18422019 - 18749808 z + 4376064 z^2 + 1802240 z^3 + 16384 z^4) BesselJ[1/4, Sqrt[z]]^2 + (122650605 + 260423856 z - 213244416 z^2 - 44605440 z^3 + 4915200 z^4 + 262144 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 6 Sqrt[z] (40883535 - 41391504 z - 3024384 z^2 + 2375680 z^3 + 49152 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]