# Fourier-Bessel series

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## Fourier-Bessel series

[‚fu̇r·ē‚ā ¦bes·əl ‚sir·ēz]
(mathematics)
For a function ƒ(x), the series whose m th term is am J0(jm x), where j1, j2, … are positive zeros of the Bessel function J0 arranged in ascending order, and am is the product of 2/ J12(jm ) and the integral over t from 0 to 1 of t ƒ(t) J0(jm t); J1 is a Bessel function.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
We obtain the energies and wave functions of reduced two-dimensional Schrodinger equation by using the double Fourier-Bessel series expansion method.
These properties of functions [a.sup.(i).sub.m] (r), i = 1, 2, are sufficient in order to expand them into Fourier-Bessel series
In conventional Fourier-Bessel series expansion, the frequency resolution of the Bessel function basis (1/2T Hz) is fixed and imprecise.
in this study, the authors used the Fourier-Bessel series and approximated the half space as a large-diameter elastic cylinder.
[7] gave another method to compute zero-order quasi-discrete HT by approximating the input function by a Fourier-Bessel series over a finite integration interval.
It is identical to our LFE-FC-7 stencil in Section 4.1 derived from using a spherical Fourier-Bessel series (SFBS).
The longitudinal components of the fields are developed into the Fourier-Bessel series. The transverse components of the fields are expressed as functions of the longitudinal components in the Laplace plane and are obtained by using the inverse Laplace transform by the residue method.
Therefore, we can consider [p.sub.m] the expansion coefficients for the Fourier-Bessel series.
Exact solutions were obtained as infinite Fourier-Bessel series. Wood [6] has considered the general case of helical flow of an Oldroyd-B fluid, due to the combined action of rotating cylinders (with constant angular velocities) and a constant axial pressure gradient.
Reducing the Gibbs phenomenon in a Fourier-Bessel series, Hankel and Fourier transform.
Given f and its Fourier-Bessel series f(x) ~ [[summation].sup.[infinity].sub.n=1] [a.sup.v.sub.n] [[phi].sup.v.sub.n](x) we consider partial sum operators
For the 3-D homogeneous Helmholtz equation, we expand the local field at a given point by spherical Fourier-Bessel series (SFB) and through an elaborated process, derive the sixth-order accurate analytical formulation, called LFE3D-27.
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