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SIGMA 4 (2008), 091, 13 pages arXiv:0812.4365
https://doi.org/10.3842/SIGMA.2008.091
Contribution to the Special Issue on Dunkl Operators and Related Topics
External Ellipsoidal Harmonics for the Dunkl-Laplacian
Hans Volkmer
Department of Mathematical Sciences,
University of Wisconsin-Milwaukee, P. O. Box 413, Milwaukee, WI 53201, USA
Received September 22, 2008, in final form December 18, 2008; Published online December 23, 2008
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
Pnα,β and Jacobi's functions
Qnα,β of the second kind.
Key words:
external ellipsoidal harmonics; Stieltjes polynomials; Dunkl-Laplacian; fundamental solution; Niven's formula; Jacobi's function of the second kind.
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