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.
References in periodicals archive ?
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.
7a) is the well-known spherical Fourier-Bessel series given by:
One of the methods to obtain LFE2D-9 equation is to solve the 8-by-8 linear equation which connects the truncated Fourier-Bessel series with the eight surrounding points on the boundary of the basic square patch.
The longitudinal components of the fields are developed into the Fourier-Bessel series.
z]) are developed into Fourier-Bessel series [12], as follows:
Based on the Fourier-Bessel series, the magnetic vector potential [A.
m] the expansion coefficients for the Fourier-Bessel series.
Reducing the Gibbs phenomenon in a Fourier-Bessel series, Hankel and Fourier transform.
Given f and its Fourier-Bessel series f(x) ~ [[summation].
o] in [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] whose Fourier-Bessel series [[summation].
Stempak proves a maximal inequality for the partial sum operator of Fourier-Bessel series in weighted Lebesgue spaces and deduces divergence and convergence results.