Eigenvalues and Eigenfunctions of the Spheroidal Wave Equation

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Abstract
A technique is presented for the calculation of the oblate and prolate spheroidal wave equation eigenvalues and eigenfunctions. The eigenvalue problem is cast in matrix form and a tridiagonal, symmetric matrix is obtained. This formulation permits the immediate calculation of the eigenvalues to the desired accuracy by means of the bisection method. The eigenfunction expansion coefficients are then obtained by a recursion method. This technique is quite simple to program, and the computation speed is rapid enough to allow its use as a function subroutine where values not previously tabulated or large numbers of values are required.

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