Hankel transform


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Hankel transform

[′häŋk·əl ‚tranz‚fȯrm]
(mathematics)
The Hankel transform of order m of a real function ƒ(t) is the function F (s) given by the integral from 0 to ∞ of ƒ(t) tJ m (st) dt, where J m denotes the m th-order Bessel function. Also known as Bessel transform; Fourier-Bessel transform.
References in periodicals archive ?
2], then the Dunkl transform is related closely to the Hankel transform on the real line.
The Hankel transform (the sequence of determinants of Hankel matrixes) ([d.
In Section 5, more properties of translated Dowling polynomials and numbers are presented, and in Section 6, we obtain the Hankel transform of the translated Dowling numbers.
The Hankel transform of an integer sequence and some of its properties were discussed by Layman in [11].
The properties of the elegant Laguerre-Gaussian beams propagating in free space [2-4], through a paraxial ABCD optical system [5], in apertured fractional Hankel transform systems [6], through aligned and misaligned paraxial optical systems [7], at a dielectric interface [8], in turbulent atmosphere [9], in non-Kolmogorov turbulence [10], by an opaque obstacle [11], and in a uniaxial crystal [12] have been extensively investigated.
First employing Hankel transform with respect to the variable r, which is denoted by * and then Laplace transform with respect to the variable z, which is denoted by--.
In this paper, we study the properties of the eigenfunctions of the finite Hankel transform.
The Hankel transform and mode-matching technique [11-13] allow us to formulate the scattered fields in analytic representations.
In the following we shall use the Laplace transform to eliminate the time variable and the finite Hankel transform for the spatial variable.
Hankel transform pairs that are useful in a wide range of physical problems with an axial symmetry are represented in cylindrical coordinates as
Shahani and Nabavi [3] solved transiented thermoelasticity problem in an isotropic thick-walled cylinder analytically by using the finite Hankel transform.
1975, "On the Hankel transform of distributions", Tohoku Math.