Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ae3l)

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

For fixed z and a₁=11/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.ae3l.01

Input Form

HypergeometricPFQ[{11/4}, {11/2, -(15/4)}, -z] == (1/(2464 Sqrt[2] z^(13/4))) ((28 z (-142760475 + 23072400 z - 1238784 z^2 + 20480 z^3) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (4996616625 - 1251677700 z + 99960000 z^2 - 2903040 z^3 + 16384 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-24983083125 + 8479107000 z - 980179200 z^2 + 43868160 z^3 - 622592 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]