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

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-7/2

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

Input Form

HypergeometricPFQ[{19/4}, {-(7/2), 21/4}, -z] == -((221 (6 Sqrt[z] (49428193815 + 42954967440 z - 14342549760 z^2 + 1817333760 z^3 - 143196160 z^4 + 9437184 z^5) BesselJ[1/4, Sqrt[z]]^2 + (-741422907225 - 1171558578960 z + 550056165120 z^2 - 88795238400 z^3 + 7983267840 z^4 - 563085312 z^5 + 16777216 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] - 6 Sqrt[z] (-247140969075 + 136714541040 z - 27965203200 z^2 + 2996613120 z^3 - 222494720 z^4 + 11534336 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(2119434240 Sqrt[2] z^(15/4)))

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]