External Ellipsoidal Harmonics for the Dunkl-Laplacian

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.

This is a contribution to the Special Issue on Dunkl Operators and Related Topics, published in SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) at http://www.emis.de/journals/SIGMA/

References in corpus (1)

• Generalized Ellipsoidal and Sphero-Conal Harmonics