New method for computing expansion coefficients for spheroidal functions

An efficient and reliable method is presented for computing the expansion c oefficients 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 n ew 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 perfor med using readily available computer library routines. The new method is sh own to produce accurate expansion coefficients for the spheroidal functions required to study scattering by particles with a wide range of shapes, siz es, and complex refractive indices. (C) 1999 Elsevier Science Ltd. All righ ts reserved.