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Power series expansions for Mathieu functions with small arguments


Authors: G. C. Kokkorakis and J. A. Roumeliotis
Journal: Math. Comp. 70 (2001), 1221-1235
MSC (2000): Primary 33E10
DOI: https://doi.org/10.1090/S0025-5718-00-01227-8
Published electronically: February 23, 2000
MathSciNet review: 1709153
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Abstract | References | Similar Articles | Additional Information

Abstract:

Power series expansions for the even and odd angular Mathieu functions $\operatorname{Se}_m(h,\operatorname{cos}\theta)$ and $\operatorname{So}_m(h,\operatorname{cos}\theta)$, with small argument $h$, are derived for general integer values of $m$. The expansion coefficients that we evaluate are also useful for the calculation of the corresponding radial functions of any kind.


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Additional Information

G. C. Kokkorakis
Affiliation: Department of Electrical and Computer Engineering, National Technical University of Athens, Athens 15773, Greece

J. A. Roumeliotis
Affiliation: Department of Electrical and Computer Engineering, National Technical University of Athens, Athens 15773, Greece
Email: iroumel@cc.ece.ntua.gr

DOI: https://doi.org/10.1090/S0025-5718-00-01227-8
Received by editor(s): May 19, 1998
Received by editor(s) in revised form: April 13, 1999, and July 8, 1999
Published electronically: February 23, 2000
Article copyright: © Copyright 2000 American Mathematical Society