Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afx3)

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.afx3.01

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), -(9/4)}, -z] == (1/(4652022375 Sqrt[2])) (z^(1/4) ((4652022375 - 11277630000 z + 10626033600 z^2 - 8554291200 z^3 - 2280337920 z^4 + 2144624640 z^5 - 730726400 z^6 + 2097152 z^7) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (4652022375 - 7556012100 z + 4912034400 z^2 - 2566589760 z^3 - 3818142720 z^4 - 1411891200 z^5 + 33292288 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 4 z (4652022375 - 3834394200 z + 2175329520 z^2 + 1496396160 z^3 - 223856640 z^4 + 174489600 z^5 - 524288 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]