Semiclassical theory for the spheroidal angular and radial functions

Here we review our study related to the accurate calculation of the angular and the radial spheroidal functions using semiclassical methods. On other words, based on Olver´s theory [1974] to asymptotic solutions of the differential equations, we show that the solution,., of the Helmholtz wave equation in the spheroidal coordinate system call be obtained using uniform asymptotic methods. These methods permit us accurately interpolate in real plane the spheroidal angular function with Weber´s parabolic cylindric functions and Legendre´s functions as well as the radial functions are well interpolated using Airy´s functions.