Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9nn)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9nn.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, -(15/4)}, -z] == ((4 z (-314786847375 - 3633903000 z - 1097026560 z^2 + 948584448 z^3 - 78249984 z^4 + 2097152 z^5) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-524644745625 + 40578583500 z - 1028160000 z^2 + 510074880 z^3 - 40042496 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-7869671184375 + 1308205080000 z - 45611748000 z^2 - 7567257600 z^3 + 4037345280 z^4 - 319291392 z^5 + 8388608 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (1599000480 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]