External Ellipsoidal Harmonics for the Dunkl-Laplacian

Details External Ellipsoidal Harmonics for the Dunkl-Laplacian External Ellipsoidal Harmonics for the Dunkl-Laplacian

2008-12-23

arxiv.org/abs/0812.4365v1

SIGMA 4 (2008), 091, 13 pages

Mathematics

Classical Analysis and ODEs

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability

Scientific paper

10.3842/SIGMA.2008.091

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.

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