Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aay9)

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aay9.01

Input Form

HypergeometricPFQ[{-(3/4)}, {9/2, -(17/4)}, -z] == -((1/(28132416 Sqrt[2] z^(11/4))) (7 (4 z (-422463195 + 28034424 z - 3508864 z^2 + 229376 z^3) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (1267389585 - 325510812 z + 10991424 z^2 - 114688 z^3) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (-3802168755 + 1700755056 z - 181358496 z^2 - 12228096 z^3 + 917504 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]