Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vr)

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`=11/2

http://functions.wolfram.com/07.22.03.a7vr.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, -(11/4)}, -z] == -(((4 z (6324353933625 + 775399716000 z + 14857678080 z^2 - 225397186560 z^3 + 54176317440 z^4 - 7061110784 z^5 + 1291845632 z^6 + 67108864 z^7) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (10540589889375 + 355391536500 z + 167009169600 z^2 - 143434152960 z^3 + 30911283200 z^4 - 4046192640 z^5 + 616562688 z^6 + 33554432 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (158108848340625 - 8723246805000 z + 1550799432000 z^2 + 1054316390400 z^3 - 1101023723520 z^4 + 242166005760 z^5 - 31855738880 z^6 + 4966055936 z^7 + 268435456 z^8) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(346983104160 Sqrt[2] z^(13/4)))

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]