*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.

## Download

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

paper_11.pdf | 281 KB | Preprint (PDF, 18 Pages) |

## 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}, }