New method for computing expansion coefficients for spheroidal functions

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.