Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7997)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.7997.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), -(21/4)}, -z] == -((1/(197358525 Sqrt[2])) (z^(1/4) ((-197358525 + 346682700 z - 148430880 z^2 - 2548800 z^3 - 584704 z^4 - 147456 z^5 + 262144 z^6) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (197358525 - 188795880 z + 11428560 z^2 - 6528 z^3 - 38912 z^4 + 32768 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 4 z (-197358525 + 30909060 z - 735696 z^2 - 111360 z^3 - 53248 z^4 + 65536 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]