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- W2026842952 abstract "It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator. In this paper we present a study of classical orthogonal polynomials in a more general context by using the differential (or difference) calculus and Operator Theory. In such a way we obtain a unified representation of them. Furthermore, some well known results related to the Rodrigues operator are deduced. A more general characterization Theorem that the one given in [1] and [2] for the q-polynomials of the q-Askey and Hahn Tableaux, respectively, is established. Finally, the families of Askey-Wilson polynomials, q-Racah polynomials, Al-Salam & Carlitz I and II, and q-Meixner are considered. [1] R. Alvarez-Nodarse. On characterization of classical polynomials. J. Comput. Appl. Math., 196:320{337, 2006. [2] M. Alfaro and R. Alvarez-Nodarse. A characterization of the classical orthogonal discrete and q-polynomials. J. Comput. Appl. Math., 2006. In press." @default.
- W2026842952 created "2016-06-24" @default.
- W2026842952 creator A5021513952 @default.
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- W2026842952 date "2009-07-04" @default.
- W2026842952 modified "2023-10-18" @default.
- W2026842952 title "q-Classical Orthogonal Polynomials: A General Difference Calculus Approach" @default.
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- W2026842952 doi "https://doi.org/10.1007/s10440-009-9536-z" @default.
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