Аннотация:
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.
Ключевые слова:external ellipsoidal harmonics; Stieltjes polynomials; Dunkl–Laplacian; fundamental solution; Niven’s formula; Jacobi’s function of the second kind.
Полный текст:
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