NEW METHOD TO OBTAIN SMALL PARAMETER POWER SERIES EXPANSIONS OF MATHIEU RADIAL AND ANGULAR FUNCTIONS

摘要

Small parameter power series expansions for both radial and angular Mathieu functions are derived. The expansions are valid for all integer orders and apply the Stratton-Morse-Chu normalization. Three new contributions are provided: ( 1) explicit power series expansions for the radial functions, which are not available in the literature; ( 2) improved convergence rate of the power series expansions of the radial functions, obtained by representing the radial functions as a series of products of Bessel functions; ( 3) simpler and more direct derivations for the power series expansion for both the angular and radial functions. A numerical validation is also given.