Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aay5)

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.aay5.01

Input Form

HypergeometricPFQ[{-(3/4)}, {9/2, -(21/4)}, -z] == (1/(9377472 Sqrt[2] z^(11/4))) ((4 z (1642912425 - 150209136 z + 10629888 z^2 - 458752 z^3) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-4928737275 + 1389434508 z - 61921152 z^2 + 455680 z^3) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (14786211825 - 6984724824 z + 833418432 z^2 + 21479424 z^3 - 1835008 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]