Abstract
We consider a conjecture on the sum of eigenvalues of two integral operators arising in potential and scattering theory for the case that the underlying surface is a triaxial ellipsoid. This concerns computation of Lamé functions which are anyway of great interest in electromagnetics and mechanics. We provide a new effective scheme for the numerical treatment of these special functions. It involves computing the Lamé functions with high accuracy combined with safe error estimates.
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Dobner, HJ., Ritter, S. Attacking a Conjecture in Mathematical Physics by Combining Methods of Computational Analysis and Scientific Computing. Reliable Computing 3, 287–295 (1997). https://doi.org/10.1023/A:1009927009271
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DOI: https://doi.org/10.1023/A:1009927009271