External Ellipsoidal Harmonics for the Dunkl-Laplacian

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.