Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afj1)

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=19/4, b_1`>=-11/2

For fixed z and a₁=19/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.afj1.01

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), 13/4}, -z] == -((1/(37255680 Sqrt[2] z^(7/4))) ((2 Sqrt[z] (122650605 + 35426160 z - 108218880 z^2 + 20275200 z^3 + 5701632 z^4 + 262144 z^5) BesselJ[1/4, Sqrt[z]]^2 + 3 (-204417675 - 266500080 z + 267886080 z^2 - 114892800 z^3 - 15400960 z^4 + 786432 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (613253025 - 508772880 z + 231390720 z^2 + 1843200 z^3 - 6389760 z^4 - 262144 z^5) 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]