New method for computing expansion coefficients for spheroidal functions.

Details New method for computing expansion coefficients for spheroidal functions. New method for computing expansion coefficients for spheroidal functions.

Dec 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999jqsrt..63..191e&link_type=abstract

Journal of Quantitative Spectroscopy and Radiative Transfer, vol. 63, issue 2-6, pp. 191-203

Statistics

Computation

4

Scattering: Numerical Methods

Scientific paper

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.

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