Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9859)

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`=-5/2

http://functions.wolfram.com/07.22.03.9859.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(5/2), 17/4}, -z] == -(((2 Sqrt[z] (406586755575 + 597112916400 z - 99672249600 z^2 - 208224276480 z^3 + 74438737920 z^4 - 12825133056 z^5 + 6593445888 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 - 3 (677644592625 + 1477068793200 z + 361686124800 z^2 - 316201881600 z^3 + 93637509120 z^4 - 18198036480 z^5 + 6358564864 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (2032933777875 + 94280986800 z + 223060780800 z^2 - 290080051200 z^3 + 89738772480 z^4 - 17505976320 z^5 + 6392119296 z^6 + 268435456 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(326998425600 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]