Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag7j)

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`=5/2

http://functions.wolfram.com/07.22.03.ag7j.01

Input Form

HypergeometricPFQ[{21/4}, {5/2, -(17/4)}, -z] == (1/(131870700 Sqrt[2] z^(3/4))) ((-8 z (-35916135 + 55721280 z + 11727360 z^2 - 131072 z^3 + 65536 z^4) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (116593785 - 339470400 z + 22510080 z^2 + 27262976 z^3 + 2686976 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (349781355 - 689424120 z + 430924800 z^2 + 119869440 z^3 + 1507328 z^4 + 524288 z^5) 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]