Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the accurate computation of the prolate spheroidal radial functions of the second kind

Authors: T. Do-Nhat and R. H. MacPhie
Journal: Quart. Appl. Math. 54 (1996), 677-685
MSC: Primary 33C05; Secondary 33C45, 65D20
DOI: https://doi.org/10.1090/qam/1417231
MathSciNet review: MR1417231
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Abstract: The series expansion of the prolate radial functions of the second kind, expressed in terms of the spherical Neumann functions, converges very slowly when the spheroid's surface coordinate $ \xi $ approaches 1 (thin spheroids). In this paper an analytical series expansion in powers of $ \left( {{\xi ^2} - 1} \right)$ is obtained to facilitate the convergence. Then, by using the Wronskian test, it is shown that this newly developed expansion has been computed with a double precision accuracy.

References [Enhancements On Off] (What's this?)

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DOI: https://doi.org/10.1090/qam/1417231
Article copyright: © Copyright 1996 American Mathematical Society

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