Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a99v)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a99v.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(11/2), 17/4}, -z] == (13 (2 Sqrt[z] (-399227719275 - 466399367280 z + 1364977152 z^2 + 10110836736 z^3 - 707985408 z^4 + 13631488 z^5) BesselJ[1/4, Sqrt[z]]^2 - 3 (-665379532125 - 1250491057200 z + 132571676160 z^2 + 9842122752 z^3 - 719912960 z^4 + 13631488 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-1996138596375 + 506955834000 z - 34887283200 z^2 + 10655244288 z^3 - 718209024 z^4 + 13631488 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(223812255744 Sqrt[2] z^(11/4))

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]