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Zbl 1204.33024
Larsen, T.M.; Erricolo, D.; Uslenghi, P.L.E.
New method to obtain small parameter power series expansions of Mathieu radial and angular functions. (English)
[J] Math. Comput. 78, No. 265, 255-274 (2009). ISSN 0025-5718; ISSN 1088-6842/e

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.

MSC 2000:: *33E10 Spheroidal wave functions, etc.

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