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

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

For fixed z and a₁=11/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{11/4}, {-(11/2), -(19/4)}, -z] == (1/(14371451325 z^(1/4))) (Sqrt[2] (3 (4790483775 + 9076706100 z + 2241162000 z^2 - 1754121600 z^3 + 389410560 z^4 - 57716736 z^5 - 35323904 z^6 + 19922944 z^7) BesselJ[1/4, Sqrt[z]]^2 - 4 Sqrt[z] (14371451325 + 8068183200 z - 7683984000 z^2 + 2049062400 z^3 - 328204800 z^4 + 39739392 z^5 - 83755008 z^6 + 2097152 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 12 z (-4790483775 + 3697917300 z - 1152597600 z^2 + 209563200 z^3 - 31933440 z^4 + 8830976 z^5 + 4456448 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]