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

Date: 2016..10..20
Event: Gama seminar
Venue: Room 2.2.D08, Math department. Universidad Carlos III de Madrid

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.

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