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On the computation of Lamé functions, of eigenvalues and eigenfunctions of some potential operators. (English) Zbl 0908.31002
The author studies in an interesting way two eigenvalue problems for the double-layer potential operator and the electrostatic integral operator. This study is based on ellipsoidal coordinates, Lamé functions of first and second kind and of surface ellipsoidal harmonics. An effective numerical computation of Lamé functions is discussed with applications to eigenvalues of the electrostatic operator. A further study is needed to extend the ideas for the numerical computation of surface ellipsoidal wave functions, which are important for scattering problems involving ellipsoids.
31B10Integral representations of harmonic functions (higher-dimensional)
33E10Lamé, Mathieu, and spheroidal wave functions
35Q60PDEs in connection with optics and electromagnetic theory
78A30Electro- and magnetostatics
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