A New Integral Equation for the Spheroidal Equations in Case of m Equal to 1

Abstract

The spheroidal wave functions are investigated in the case $ m = 1$. The integral equation is obtained for them. There are two kinds of eigenvalues in the differential and corresponding integral equations, and the relation between them is given explicitly. This is the great advantage of our integral equation, which will provide useful information through the study of the integral equation. Also an example is given for the special case, which shows another way to study the eigenvalue problem.