GENERALIZED DISCRETE FOURIER-TRANSFORMS - THE DISCRETE FOURIER-RICCATI-BESSEL TRANSFORM

We present and demonstrate a discrete Fourier-Riccati-Bessel transform that incorporates Neumann boundary conditions. We also suggest that this methodology, which originated with H.F. Johnson, can be applied to other discrete Fourier-type transforms with different boundary conditions. This project was originally motivated by the development of the generalized Fourier-grid R-matrix scattering method. We present the transform itself, its derivation, analysis of the approximations involved, and some applications.