Second structure relation for $q$-semiclassical polynomials of the Hahn Tableau
Classical Analysis and ODEs
2009-04-18 v1
Abstract
The 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.
Cite
@article{arxiv.0807.1353,
title = {Second structure relation for $q$-semiclassical polynomials of the Hahn Tableau},
author = {R. S. Costas-Santos and F. Marcellan},
journal= {arXiv preprint arXiv:0807.1353},
year = {2009}
}
Comments
Keywords: Finite-type relation; Recurrence relation; q-Polynomials; q-Semiclassical polynomials