Dunkl - Semiclassical Orthogonal Polynomials . the Symmetric Case
نویسنده
چکیده
where A and B are fixed polynomials with degA ≤ 2, and degB = 1. In 1939, Shohat extended these ideas introducing a new class of orthogonal polynomials. In fact, he studied orthogonal polynomials associated with forms satisfying the last equation, with no restrictions in the degrees of the polynomials A, and B. Obviously, orthogonal polynomials defined as above, generalize in a natural way the classical ones. They were called semiclassical orthogonal polynomials [15]. Among others, an approach to such polynomials taking into account
منابع مشابه
Characterization of the Dunkl-classical symmetric orthogonal polynomials
In this paper, we introduce the notion of Dunkl-classical orthogonal polynomials. Then, we show that generalized Hermite and generalized Gegenbauer polynomials are the only Dunkl-classical symmetric orthogonal polynomials by solving a suitable differential-difference equation. 2006 Elsevier Inc. All rights reserved.
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