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

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`=11/2

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

Input Form

HypergeometricPFQ[{19/4}, {11/2, -(19/4)}, -z] == (1/(7724640 Sqrt[2] z^(13/4))) ((4 z (-776474223525 + 178545767400 z - 17732897280 z^2 + 1054126080 z^3 - 42663936 z^4 + 524288 z^5) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-1294123705875 + 412609497300 z - 52079731200 z^2 + 3676968960 z^3 - 174325760 z^4 + 4456448 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-19411855588125 + 7914640734000 z - 1272350570400 z^2 + 108793036800 z^3 - 5950586880 z^4 + 212336640 z^5 - 2097152 z^6) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^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]