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Symmetry, Integrability and Geometry: Methods and Applications, 2006, Volume 2, 071, 16 pp.
DOI: https://doi.org/10.3842/SIGMA.2006.071 (Mi sigma99) 		 
This article is cited in 7 scientific papers (total in 7 papers)

Generalized Ellipsoidal and Sphero-Conal Harmonics

Hans Volkmer

Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, WI 53201 USA
Full-text PDF (286 kB) Citations (7)
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DOI: https://doi.org/10.3842/SIGMA.2006.071
Abstract: Classical ellipsoidal and sphero-conal harmonics are polynomial solutions of the Laplace equation that can be expressed in terms of Lamé 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.
Keywords: generalized ellipsoidal harmonic; Stieltjes polynomials; Dunkl equation; Niven formula.
Received: August 25, 2006; in final form October 20, 2006; Published online October 24, 2006
Bibliographic databases:
Document Type: Article
MSC: 33C50; 35C10
Language: English
Citation: Hans Volkmer, “Generalized Ellipsoidal and Sphero-Conal Harmonics”, SIGMA, 2 (2006), 071, 16 pp.
Citation in format AMSBIB
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