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 , as follows:
Based on the Fourier-Bessel series, the magnetic vector potential [A.
m] the expansion coefficients for the Fourier-Bessel series.
Exact solutions were obtained as infinite 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.