Some Relations Between the Spheroidal and Spherical Wave Functions

Abstract

New relations are found between the spheroidal and spherical wave functions, as well as between the spheroidal functions related to different spheroidal coordinate systems. The systems must have a common origin of coordinates and a common symmetry axis of coordinate surfaces. The applicability ranges of the relations obtained are discussed. Numerical test calculations have demonstrated a high efficiency of the relations, specifically those for wave functions including the radial functions of the first kind. As a particular case, relations are considered between prolate and oblate spheroidal wave functions including radial functions of the first and second kinds. These relations are necessary for solving the light scattering problem for nonconfocal layered spheroidal particles. Bibliography: 15 titles.