Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7uv)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7uv.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 5/4}, -z] == ((4 z (253746675 + 45919243440 z + 91808952984 z^2 + 34095995136 z^3 + 3034128384 z^4 + 78053376 z^5 + 524288 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (422911125 + 451105200 z + 32990649300 z^2 + 15776474112 z^3 + 1483302912 z^4 + 38797312 z^5 + 262144 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (6343666875 + 6202696500 z + 12630945600 z^2 + 276004078560 z^3 + 127582608384 z^4 + 11904417792 z^5 + 310640640 z^6 + 2097152 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (91252050120 Sqrt[2] z^(9/4))

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]