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# Orthogonality of q-polynomials for nonstandard parameters

Orthogonality of q-polynomials for nonstandard parameters

Date: 2011..03..17
Event: Gama seminar
Venue: Room 2.2.D08, Math department. Universidad Carlos III de Madrid

## Abstract

$$q$$-Classical orthogonal polynomials of the $$q$$-Hahn tableau are characterized from their orthogonality condition and by a first and a second structure relation. Unfortunately, for the q-semiclassical orthogonal polynomials (a generalization of the classical ones) we find only in the literature the first structure relation.

In this talk we present a second structure relation. In particular, by means of a general finite-type relation between a $$q$$-semiclassical polynomial sequence and the sequence of its $$q$$-differences such a structure relation is obtained.