New method to obtain small parameter power series expansions of Mathieu radial and angular functions

Larsen, T.; Erricolo, D.; Uslenghi, P.

doi:10.1090/S0025-5718-08-02114-5

New method to obtain small parameter power series expansions of Mathieu radial and angular functions
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by T. M. Larsen, D. Erricolo and P. L. E. Uslenghi PDF

Math. Comp. 78 (2009), 255-274 Request permission

Abstract:

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.

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