Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adm3)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.adm3.01

Input Form

HypergeometricPFQ[{9/4}, {9/2, -(21/4)}, -z] == (1/(636480 Sqrt[2] z^(11/4))) ((4 z (14786211825 - 3379705560 z + 261624960 z^2 - 7055360 z^3 + 32768 z^4) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (44358635475 - 18588380580 z + 2276735040 z^2 - 103418880 z^3 + 1359872 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (133075906425 - 81112933440 z + 16135368480 z^2 - 1157875200 z^3 + 29614080 z^4 - 131072 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]