Second structure relation for $q$-semiclassical polynomials of the Hahn Tableau

Details Second structure relation for $q$-semiclassical polynomials of the Hahn Tableau Second structure relation for $q$-semiclassical polynomials of the Hahn Tableau

2008-07-08

arxiv.org/abs/0807.1353v1

J. Math. Anal. Appl. 329(1) (2007), 206-228

Mathematics

Classical Analysis and ODEs

Keywords: Finite-type relation; Recurrence relation; q-Polynomials; q-Semiclassical polynomials

Scientific paper

10.1016/j.jmaa.2006.06.036

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.

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