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.
Keywords:external ellipsoidal harmonics; Stieltjes polynomials; Dunkl–Laplacian; fundamental solution; Niven’s formula; Jacobi’s function of the second kind.
Fulltext:
PDF file (268 kB)
