Analytic properties of some basic hypergeometric- Sobolev-type orthogonal polynomials

Abstract

In this contribution, we consider sequences of monic basic hypergeometric-Sobolev-type orthogonal polynomials where u is a q-classical linear functional and Dq is the q-derivative operator. We obtain some algebraic properties of these polynomi- als such as an explicit representation, a five-term recurrence relation as well as a second order linear q-difference holonomic equation ful- filled by such polynomials. We present an analysis of the behaviour of its zeros as a function of the mass N. In particular, we obtain the exact values of N such that the smallest (respectively, the greatest) zero of the studied polynomials is located outside of the support of the measure. We conclude this work by considering two examples.

Es la versión preprint del artículo. Se puede consultar la versión final en https://doi.org/10.1080/10236198.2018.1517760