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SIGMA 2 (2006), 071, 16 pages math.CA/0610718
https://doi.org/10.3842/SIGMA.2006.071
Contribution to the Vadim Kuznetsov Memorial Issue
Generalized Ellipsoidal and Sphero-Conal Harmonics
Hans Volkmer
Department of Mathematical Sciences, University of Wisconsin-Milwaukee,
P.O. Box 413, Milwaukee, WI 53201 USA
Received August 25, 2006, in final form October 20, 2006; Published online October 24, 2006
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.
Key words:
generalized ellipsoidal harmonic; Stieltjes polynomials; Dunkl equation; Niven formula.
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