Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afx7)

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.afx7.01

Input Form

HypergeometricPFQ[{21/4}, {-(11/2), -(5/4)}, -z] == (1/(516891375 Sqrt[2])) (z^(1/4) ((516891375 - 1428499800 z + 2506140000 z^2 + 634233600 z^3 - 1174394880 z^4 - 353206272 z^5 + 14680064 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (516891375 - 1014986700 z + 831448800 z^2 + 1312637760 z^3 + 217580544 z^4 + 63815680 z^5 - 262144 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (-516891375 + 601473600 z + 512431920 z^2 - 225775872 z^3 - 73224192 z^4 + 3604480 z^5) 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]