Paper: Orthogonality of q-polynomials for non-standard parameters

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},
}