Generalized Ellipsoidal and Sphero-Conal Harmonics

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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.
This is a contribution to the Vadim Kuznetsov Memorial Issue on Integrable Systems and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

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Classical Analysis and ODEs, Mathematical Physics

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http://salesiana.dossiersoluciones.com/handle/123456789/159531

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0610718
 http://arxiv.org/abs/math/0610718
 SIGMA 2 (2006), 071, 16 pages
 doi:10.3842/SIGMA.2006.071

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