Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8pb)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a8pb.01

Input Form

HypergeometricPFQ[{-(13/4)}, {7/2, -(3/4)}, -z] == -((1/(1817046 Sqrt[2] z^(5/4))) ((8 z (-392661 - 287136 z + 1522944 z^2 + 470016 z^3 + 16384 z^4) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (205335 - 1033056 z + 1135872 z^2 + 455680 z^3 + 16384 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (3080025 + 2400840 z - 8128512 z^2 + 9492480 z^3 + 3661824 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]