Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agq5)

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.agq5.01

Input Form

HypergeometricPFQ[{23/4}, {9/2, -(19/4)}, -z] == (1/(330228360 Sqrt[2] z^(9/4))) ((-4 z (-14989849875 + 4801219920 z - 1295562240 z^2 + 9805824 z^3 + 30474240 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (24983083125 - 10497942000 z + 2414845440 z^2 - 269230080 z^3 - 65994752 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (374746246875 - 190779907500 z + 45778824000 z^2 - 6993745920 z^3 - 650280960 z^4 + 128188416 z^5 + 4194304 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]