2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/213344The 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 $P_n^{α,β}$ and Jacobi's functions $Q_n^{α,β}$ 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/Classical Analysis and ODEsMathematical Physicstext