Power series expansions for Mathieu functions with small arguments

Kokkorakis, G.; Roumeliotis, J.

doi:10.1090/S0025-5718-00-01227-8

Power series expansions for Mathieu functions with small arguments
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by G. C. Kokkorakis and J. A. Roumeliotis;

Math. Comp. 70 (2001), 1221-1235

DOI: https://doi.org/10.1090/S0025-5718-00-01227-8

Published electronically: February 23, 2000

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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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