Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ag0z)

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=21/4, b_1`>=-11/2

For fixed z and a₁=21/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.ag0z.01

Input Form

HypergeometricPFQ[{21/4}, {-(5/2), -(13/4)}, -z] == -((1/(87267375 Sqrt[2])) (z^(1/4) ((-87267375 + 230922900 z - 269708400 z^2 + 392071680 z^3 + 2851430400 z^4 - 340656128 z^5 + 1048576 z^6) BesselJ[-(1/4), Sqrt[z]]^ 2 + 12 Sqrt[z] (-29089125 + 53703000 z - 49008960 z^2 + 95047680 z^3 - 248004608 z^4 + 5242880 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (87267375 - 91295100 z + 80196480 z^2 + 545789952 z^3 - 81297408 z^4 + 262144 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]