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

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.afkd.01

Input Form

HypergeometricPFQ[{19/4}, {-(7/2), 13/4}, -z] == (1/(2069760 Sqrt[2] z^(7/4))) ((-2 Sqrt[z] (4542615 + 388080 z - 5322240 z^2 + 540672 z^3 + 311296 z^4) BesselJ[1/4, Sqrt[z]]^2 + (22713075 + 28440720 z - 33707520 z^2 + 14868480 z^3 + 3833856 z^4 + 262144 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-22713075 + 20013840 z - 9884160 z^2 - 1044480 z^3 + 212992 z^4) 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]