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

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=1/4, b_1`>=-11/2

For fixed z and a₁=1/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{1/4}, {-(11/2), 15/4}, -z] == (1/(23592960 Sqrt[2] z^(9/4))) ((2 Sqrt[z] (-2331754425 + 2261095200 z - 163872000 z^2 + 2883584 z^3) BesselJ[-(1/4), Sqrt[z]]^2 + (6995263275 - 17442734400 z + 3332609280 z^2 - 122880000 z^3 + 524288 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 90 Sqrt[z] (-155450295 + 55989024 z - 5148416 z^2 + 65536 z^3) 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]