New methods for treatment of spheroidal functions in the solution of scalar wave equation

Abstract

In this paper we propose two new analitical and numerical methods, useful for calculating the spheroidal functions. An algorithm for the evaluation of the expansion coefficient of angle functions in series of associated Legendre functions, as well as for the calculations of the eigenvalue, is developed. The coefficients of the expansion of radial functions of first and second kind in series of product of Bessel functions are explicitly calculated; a very simple expression is obtained when the differencen - m between the degree and the order is even.