**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.

## Download

Link | Size | Description |
---|---|---|

T5_SICM06.pdf | 284 KB | Slides (PDF, 22 pages, 18 slides) |