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Gegenbauer polynomials, as reproducing kernels for the spaces of spherical harmonics of a given degree, or more generally, as providing an explicit construction of symmetry
In the previous section we showed that the Christoffel transformation of Hermite’s elliptic LBP gives polynomials orthogonal on the unit circle with explicit reflection
[12] Koornwinder T.H., Askey–Wilson polynomials for root systems of type BC, in Hypergeometric Functions on Domains of Positivity, Jack Polynomials, and Applications, Editor D.St.P.
Our paper is organized as follows: In Section 2 we recollect some facts on symmetric functions, and, in particular, A n−1 Macdonald polynomials. We conclude this section by stating
Both algebras are presented by generators and relations, the first has a representation by q -difference operators on the space of symmetric Laurent polynomials in z and the second
[3] Castro M., Gr¨ unbaum F.A., The algebra of matrix valued differential operators associated to a given family of matrix valued orthogonal polynomials: five instructive examples,
Now, in view of the above, in order to solve the problem of orthogonal separability of the cor- responding Hamilton–Jacobi equation and thus find exact solutions to the
The derivation deduces Branson’s formula from knowledge of the correspon- ding conformally invariant operator on Euclidean space (the k -th power of the Euclidean Laplacian)
