*q*-Classical orthogonal polynomial: A general difference calculus approach

Costas-Santos, R. S.and Marcellan, F. **Acta Applicandae Mathematicae**111 (2010), 107 — 128

## 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 paper, a second structure relation is deduced. 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.

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## BibTeX

@article {MR2653053, AUTHOR = {Costas-Santos, R. S. and Marcellan, F.}, TITLE = {{$q$}-classical orthogonal polynomials: a general difference calculus approach}, JOURNAL = {Acta Appl. Math.}, FJOURNAL = {Acta Applicandae Mathematicae}, VOLUME = {111}, YEAR = {2010}, NUMBER = {1}, PAGES = {107--128}, ISSN = {0167-8019}, MRCLASS = {33C45 (33D45 39A13 42C05)}, MRNUMBER = {2653053}, ZBL = {1204.33011}, MRREVIEWER = {Thomas Stoll}, DOI = {10.1007/s10440-009-9536-z}, URL = {https://doi.org/10.1007/s10440-009-9536-z}, }