Second structure relation for -semiclassical polynomials of the Hahn Tableau
arXiv:0807.1353 · doi:10.1016/j.jmaa.2006.06.036
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.
Keywords: Finite-type relation; Recurrence relation; q-Polynomials; q-Semiclassical polynomials