Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9067)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9067.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(7/4)}, -z] == ((4 z (-68695568589375 - 15352914376800 z + 4389294873600 z^2 + 10989748224000 z^3 - 5278113792000 z^4 + 4639414026240 z^5 + 980532854784 z^6 + 34527510528 z^7 + 268435456 z^8) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-114492614315625 - 15411069355500 z - 5439727238400 z^2 + 9063460224000 z^3 - 4048360243200 z^4 + 1915335475200 z^5 + 475358822400 z^6 + 17146314752 z^7 + 134217728 z^8) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-1717389214734375 - 78509221245000 z - 55828779552000 z^2 - 40351660876800 z^3 + 69150877286400 z^4 - 31560302592000 z^5 + 15748772659200 z^6 + 3819605852160 z^7 + 137304735744 z^8 + 1073741824 z^9) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(18453192357600 Sqrt[2] z^(13/4))

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]