Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7ub)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7ub.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, -(15/4)}, -z] == ((4 z (-903479133375 - 18246649680 z + 220355428608 z^2 - 45912526848 z^3 + 4358995968 z^4 - 265289728 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-1505798555625 - 175388031000 z + 134954709120 z^2 - 25114146816 z^3 + 2307948544 z^4 - 139984896 z^5 + 8388608 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-22586978334375 - 623089057500 z - 1019096769600 z^2 + 1041140597760 z^3 - 197973983232 z^4 + 18297913344 z^5 - 1111490560 z^6 + 67108864 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (334590850440 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]