| Abstract: | Approximate relations are obtained between the eigenvalues λ and the ellipticity parameter c2 of the angular spheroidal wave equation. Although based on WKBJ methods and the assumption that λ is large, the relations are useful throughout the complex c2-plane. They are exact at c2 = 0, and reproduce the standard asymptotic formulas for λ when c2 is large. At intermediate values of c2, they provide approximations for the square-root branch points of the multivalued function λ(c2) in the complex c2-plane at which adjacent eigenvalues of the same class become equal in pairs. These branch points lie on an infinite sequence of distorted circular rings. Their exact locations have been computed for the first four rings for angular wavenumbers m = 0,…,4. |
