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Symmetry, Integrability and Geometry: Methods and Applications, 2008, Volume 4, 091, 13 pp.
DOI: https://doi.org/10.3842/SIGMA.2008.091 (Mi sigma344) 		 
This article is cited in 3 scientific papers (total in 3 papers)

External Ellipsoidal Harmonics for the Dunkl–Laplacian

H. Volkmer

Department of Mathematical Sciences, University of Wisconsin-Milwaukee, P. O. Box 413, Milwaukee, WI 53201, USA
Full-text PDF (268 kB) Citations (3)
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DOI: https://doi.org/10.3842/SIGMA.2008.091
Abstract: The paper introduces external ellipsoidal and external sphero-conal $h$-harmonics for the Dunkl–Laplacian. These external $h$-harmonics admit integral representations, and they are connected by a formula of Niven's type. External $h$-harmonics in the plane are expressed in terms of Jacobi polynomials $P_n^{\alpha,\beta}$ and Jacobi's functions $Q_n^{\alpha,\beta}$ of the second kind.
Keywords: external ellipsoidal harmonics; Stieltjes polynomials; Dunkl–Laplacian; fundamental solution; Niven’s formula; Jacobi’s function of the second kind.
Received: September 22, 2008; in final form December 18, 2008; Published online December 23, 2008
Bibliographic databases:
Document Type: Article
MSC: 33C52; 35C10
Language: English
Citation: H. Volkmer, “External Ellipsoidal Harmonics for the Dunkl–Laplacian”, SIGMA, 4 (2008), 091, 13 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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