New method for computing expansion coefficients for spheroidal functions

Hans A. Eide, Jakob J. Stamnes, Knut Stamnes, F. Michael Schulz

Research output: Contribution to journalArticlepeer-review

13 Scopus citations

Abstract

An efficient and reliable method is presented for computing the expansion coefficients in the eigenfunction series representing the prolate and oblate spheroidal functions. While the traditional method is based on recurrence relations, infinite continued fractions, and a variational procedure, the new method is based on reformulating the computational task as an eigenvalue problem. In contrast with the traditional method, the new method requires no initial estimates of the eigenvalues, and the computations can be performed using readily available computer library routines. The new method is shown to produce accurate expansion coefficients for the spheroidal functions required to study scattering by particles with a wide range of shapes, sizes, and complex refractive indices.

Original languageEnglish
Pages (from-to)191-203
Number of pages13
JournalJournal of Quantitative Spectroscopy and Radiative Transfer
Volume63
Issue number2-6
DOIs
StatePublished - Sep 1999

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