Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aeu5)

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=3/2

http://functions.wolfram.com/07.22.03.aeu5.01

Input Form

HypergeometricPFQ[{15/4}, {3/2, -(19/4)}, -z] == (1/(15207885 z^(1/4))) (Sqrt[2] (-9 (-1689765 - 4268880 z - 2462208 z^2 + 126976 z^3 + 65536 z^4) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-15207885 - 10624320 z + 6847488 z^2 + 1228800 z^3 + 65536 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 48 z (484155 - 834240 z - 58624 z^2 + 8192 z^3) 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]