The orthogonality relations of the Al-Salam-Carlitz polynomials for general parameters

Date: 2017..02..09
Event: Seminario TAPO
Venue: Math department. Universidad de Almeria

Abstract

In this talk we describe the orthogonality conditions satisfied by Al-Salam-Carlitz polynomials when the parameters a and a are not necessarily real nor 'classical', i.e., the linear functional u with respect to such polynomial sequence is quasi-definite and not positive definite.

We establish orthogonality on a simple contour in the complex plane which depends on the parameters. In all cases we show that the orthogonality conditions characterize the Al-Salam-Carlitz polynomials of degree n up to a constant factor. We also obtain a generalization of the unique generating function for these polynomials.

This is a joint work with Cohl, Howard S, and Wenqing Xu.

Download