Talk: Classical orthogonal polynomials. A general difference calculus approach

Date: 2006..08..31
Event: Recent Trends in Constructive Approximation Theory (IWOP'06)
Venue: Leganés, Spain

Abstract

It is well known that the classical families of orthogonal polynomials are characterized as eigenfunctions of a second order linear differential/difference operator with polynomial coefficients.

In this talk we present a study of classical orthogonal polynomials in a more general framework 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 presented.

A more general Characterization Theorem 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.

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