# Optimal cylindrical and spherical Bessel transforms satisfying bound state boundary conditions

## Description

Abstract Optimal discrete transforms based upon the radial Laplacian eigenfunctions in cyclindrical and spherical coordinates are presented, featuring the following properties: (1) bound state boundary conditions are enforced; (2) in the case of cylindrical or spherical symmetry, the relevant discrete Bessel transform (DBT) is analogous to the discrete Fourier transform in Cartesian coordinates; (3) the underlying quadrature algorithms achieve a Gaussian-like accuracy; (4) orthogonality of the transfo... Title of program: HODBT Catalogue Id: ADEX_v1_0 Nature of problem In many applications it is appropriate to expand the sought function in terms of the bounded radial eigenfuctions of the Laplacian in cylindrical or spherical coordinates. These involve Bessel functions of the first kind, Jnu, with integer or half-integer order nu, and the computation of the integral Bessel (or Hankel) transform that generally has to be discretized. Versions of this program held in the CPC repository in Mendeley Data ADEX_v1_0; HODBT; 10.1016/S0010-4655(96)00141-5 This program has been imported from the CPC Program Library held at Queen's University Belfast (1969-2019)