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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=5/2

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

Input Form

HypergeometricPFQ[{23/4}, {5/2, -(23/4)}, -z] == (1/(33229228725 z^(1/4))) (Sqrt[2] ((33229228725 + 93922370640 z + 31669424640 z^2 - 5846851584 z^3 - 1050083328 z^4 - 57671680 z^5) BesselJ[1/4, Sqrt[z]]^2 + 8 Sqrt[z] (-25472252925 - 4581727920 z + 7291307520 z^2 + 626368512 z^3 + 1507328 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 7 (12653769375 - 908830800 z - 10803755520 z^2 + 193781760 z^3 + 143327232 z^4 + 7340032 z^5) 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]