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Generalized Ellipsoidal and Sphero-Conal Harmonics

Hans Volkmer
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Abstract

Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lame polynomials. Generalized ellipsoidal and sphero-conal harmonics are polynomial solutions of the more general Dunkl equation that can be expressed in terms of Stieltjes polynomials. Niven's formula connecting ellipsoidal and sphero-conal harmonics is generalized. Moreover, generalized ellipsoidal harmonics are applied to solve the Dirichlet problem for Dunkl's equation on ellipsoids.

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BibTeXRIS

Hans Volkmer. 2006-10-24. Generalized Ellipsoidal and Sphero-Conal Harmonics. https://doi.org/10.3842/sigma.2006.071

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