Discrete semi-classical orthogonal polynomials of class one on quadratic lattices

Abstract

ABSTRACTWe study orthogonal polynomials on quadratic lattices with respect to Stieltjes functions, S, that satisfy a difference equation where A is a polynomial of degree less or equal than 3 and C is a polynomial of degree greater or equal than 1 and less or equal than 2. We show systems of difference equations for the orthogonal polynomials that arise from the so-called compatibility conditions. Some closed formulae for the recurrence relation coefficients are obtained.