Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a80h)

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`=-7/2

http://functions.wolfram.com/07.22.03.a80h.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(7/2), 15/4}, -z] == ((2 Sqrt[z] (-126638386875 + 69470200800 z + 66280032000 z^2 - 28590981120 z^3 + 4007854080 z^4 - 304087040 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (379915160625 - 787328942400 z - 97037740800 z^2 + 31801835520 z^3 - 4226088960 z^4 + 314572800 z^5 - 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (379915160625 + 23156733600 z + 75865870080 z^2 - 29742612480 z^3 + 4090429440 z^4 - 308281344 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(128817561600 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]