Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa77)

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.aa77.01

Input Form

HypergeometricPFQ[{-(5/4)}, {-(9/2), 17/4}, -z] == -((1/(462422016 Sqrt[2] z^(11/4))) (13 (2 Sqrt[z] (1267389585 + 1453636800 z - 23643648 z^2 - 19808256 z^3 + 851968 z^4) BesselJ[1/4, Sqrt[z]]^2 - 3 (2112315975 + 3924819360 z - 516848640 z^2 - 15966208 z^3 + 851968 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (6336947925 - 1744364160 z + 110753280 z^2 - 20447232 z^3 + 851968 z^4) 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]