## Orthogonality of *q*-polynomials for non-standard parameters

Costas-Santos, R. S. and Sanchez-Lara, J. F. **Journal of Approximation Theory**163, no. 9(2011), 1246 —1268

## 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 {MR2832754, AUTHOR={Costas-Santos, R. S. and Sanchez-Lara, J. F.}, TITLE={Orthogonality of {$q$}-polynomials for non-standard parameters}, JOURNAL={J. Approx. Theory}, FJOURNAL={Journal of Approximation Theory}, VOLUME={163}, YEAR={2011}, NUMBER={9}, PAGES={1246--1268}, ISSN={0021-9045}, CODEN={JAXTAZ}, MRCLASS={33D45}, MRNUMBER={2832754 (2012f:33027)}, ZBL={1229.33016}, MRREVIEWER={Ulrich Tamm}, DOI={10.1016/j.jat.2011.04.005}, URL={http://dx.doi.org/10.1016/j.jat.2011.04.005}, }