Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aei3)

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.aei3.01

Input Form

HypergeometricPFQ[{13/4}, {9/2, -(21/4)}, -z] == -((1/(5728320 Sqrt[2] z^(11/4))) ((44 z (6721005375 - 1843475760 z + 199895040 z^2 - 10465280 z^3 + 196608 z^4) BesselJ[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (-221793177375 + 103081019580 z - 15993780480 z^2 + 1170186240 z^3 - 38797312 z^4 + 262144 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (665379532125 - 435982017240 z + 100300939200 z^2 - 10108753920 z^3 + 501596160 z^4 - 8912896 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]