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

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`=-9/2

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

Input Form

HypergeometricPFQ[{21/4}, {-(9/2), 3/4}, -z] == (1/(9398025 Sqrt[2])) (z^(1/4) ((9398025 + 20884500 z - 13197600 z^2 - 8573760 z^3 - 1583104 z^4 + 16384 z^5) BesselJ[-(1/4), Sqrt[z]]^2 + 1216 z^(3/2) (61425 + 19305 z + 672 z^2 + 512 z^3) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 4 z (-9398025 + 1425060 z + 2016144 z^2 + 357888 z^3 - 4096 z^4) 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]