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New method to obtain small parameter power series expansions of Mathieu radial and angular functions. (English) Zbl 1204.33024
Summary: 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.
33E10Lamé, Mathieu, and spheroidal wave functions
Algorithm 861
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