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

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`=3/2

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

Input Form

HypergeometricPFQ[{13/4}, {3/2, 23/4}, -z] == -((1/(524288 Sqrt[2] z^(17/4))) (1463 (10 Sqrt[z] (45045 - 45936 z + 5120 z^2) BesselJ[-(1/4), Sqrt[z]]^ 2 + (-675675 + 1718640 z - 399360 z^2 + 16384 z^3) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 18 Sqrt[z] (75075 - 30800 z + 3072 z^2) 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]