Bessel function of the first kind: Integral transforms (formula 03.01.22.0005)

BesselJ

$Mathematica Notation$

Bessel-Type Functions

BesselJ[nu,z]

Integral transforms

Hankel transforms

http://functions.wolfram.com/03.01.22.0005.02

Input Form

HankelTransform[BesselJ[\[Nu], t], {t, \[Mu]}, z] == ((Sqrt[2] z^(1/2 + \[Mu]) Gamma[(3 + 2 \[Mu] + 2 \[Nu])/4] UnitStep[1 - z])/ (Gamma[1 + \[Mu]] Gamma[(1 - 2 \[Mu] + 2 \[Nu])/4])) Hypergeometric2F1[(3 + 2 \[Mu] - 2 \[Nu])/4, (3 + 2 \[Mu] + 2 \[Nu])/4, 1 + \[Mu], z^2] + ((Sqrt[2] z^(-1 - \[Nu]) Gamma[(3 + 2 \[Mu] + 2 \[Nu])/4] UnitStep[-1 + z])/(Gamma[1 + \[Nu]] Gamma[(1 + 2 \[Mu] - 2 \[Nu])/4])) Hypergeometric2F1[(3 - 2 \[Mu] + 2 \[Nu])/4, (3 + 2 \[Mu] + 2 \[Nu])/4, 1 + \[Nu], 1/z^2] /; z > 0 && z != 1 && Re[\[Nu] + \[Mu]] > -(3/2)

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)

2001-10-29