## 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}, }