Power series expansions for spheroidal wave functions with small arguments

Authors:
Gerassimos C. Kokkorakis;John A. Roumeliotis
Affiliations:
Department of Electrical and Computer Engineering, National Technical University of Athens, Athens 15773, Greece;Department of Electrical and Computer Engineering, National Technical University of Athens, Athens 15773, Greece
Venue:
Journal of Computational and Applied Mathematics
Year:
2002

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Power series expansions for Mathieu functions with small arguments

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Abstract

Power series expansions for the angular spheroidal wave functions of the first kind Smn(c,η), with small arguments c, are derived for general integer values of m and n. The various evaluated expansion coefficients can also be used in the calculation of the corresponding angular functions of the second kind, as well as for the radial functions of any kind. Only the prolate functions are considered explicitly, but corresponding formulas for the oblate ones are obtained immediately.