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

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=7/4, b_1`>=-11/2

For fixed z and a₁=7/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{7/4}, {-(11/2), -(19/4)}, -z] == (1/(2053064475 z^(1/4))) (Sqrt[2] ((2053064475 + 3968603100 z + 1104863760 z^2 - 722494080 z^3 + 137491200 z^4 - 16257024 z^5 - 2555904 z^6 + 1048576 z^7) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-2053064475 - 1231183800 z + 1058127840 z^2 - 249258240 z^3 + 33223680 z^4 - 3342336 z^5 + 2883584 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 4 z (-2053064475 + 1506235500 z - 428772960 z^2 + 66306240 z^3 - 7726080 z^4 + 1327104 z^5 + 262144 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]