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math.CA2023
The Laplace-Beltrami Operator on the Surface of the Ellipsoid
Hans Volkmer
The Laplace-Beltrami operator on (the surface of) a triaxial ellipsoid admits a sequence of real eigenvalues diverging to plus infinity. By introducing ellipsoidal coordinates, thi…
math.CA2023
On the Hill Discriminant of Lamé's Differential Equation
Hans Volkmer
Lamé's differential equation is a linear differential equation of the second order with a periodic coefficient involving the Jacobian elliptic function depending on the…
math.CA2023★ 1 cited
Internal and external harmonics in bi-cyclide coordinates
Brandon Alexander, Howard S. Cohl, Hans Volkmer
The Laplace equation in three dimensional Euclidean space is -separable in bi-cyclide coordinates leading to harmonic functions expressed in terms of Lamé-Wangerin functions cal…