Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9229)

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`=-7/2

http://functions.wolfram.com/07.22.03.9229.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(7/2), 11/4}, -z] == ((2 Sqrt[z] (-13749310575 + 37297260000 z - 29157822720 z^2 + 7063879680 z^3 - 984678400 z^4 + 132120576 z^5 + 16777216 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + (41247931725 - 41902660800 z + 34144830720 z^2 - 7706050560 z^3 + 1039073280 z^4 - 121634816 z^5 - 16777216 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + 2 Sqrt[z] (41247931725 + 46092926880 z - 31238887680 z^2 + 7330775040 z^3 - 1011154944 z^4 + 127926272 z^5 + 16777216 z^6) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(88562073600 Sqrt[2] z^(5/4))

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]