Abstract
The Laplace-Beltrami operator on a prolate spheroid admits a sequence of eigenvalues. These eigenvalues are determined by a singular Sturm-Liouville problem. Properties of the eigenvalues are obtained using the minimum-maximum principle and the Prüfer angle. In particular, eigenvalues are approximated by those of generalized matrix eigenvalue problems, and their behavior is studied when the eccentricity of the spheroid approaches 0 or 1.
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