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

Orthogonality of q-polynomials for non-standard parameters

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},
}