Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9007)

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`=9/2

http://functions.wolfram.com/07.22.03.9007.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, -(19/4)}, -z] == -(((4 z (626111039428875 + 15235620901200 z - 146476929312000 z^2 + 29630241607680 z^3 - 2682027048960 z^4 + 148173225984 z^5 - 5989466112 z^6 + 268435456 z^7) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (1043518399048125 + 118054606761000 z - 89076844886400 z^2 + 16127171020800 z^3 - 1411140648960 z^4 + 76905185280 z^5 - 3112173568 z^6 + 134217728 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (15652775985721875 + 379461236017500 z + 683902549512000 z^2 - 688141231948800 z^3 + 127248603955200 z^4 - 11199448350720 z^5 + 611718266880 z^6 - 24763170816 z^7 + 1073741824 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (222502915542600 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]