Center for Mathematics, University of Coimbra

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Publications

The Symmetric Semi-classical Orthogonal Polynomials of Class Two and Some of Their Extensions

Publication . Rebocho, M. N.; Filipuk, Galina

We study a large class of orthogonal polynomials, containing the semi-classical symmetric orthogonal polynomials of class two. We show difference equations for the recurrence coefficients of the orthogonal polynomials as well as for related quantities. Some of these recurrences are identified with discrete Painlevé equations.

2019Preprint

Open access

On the second order holonomic equation for Sobolev-type orthogonal polynomials

Publication . Rebocho, Maria das Neves

It is presented a general approach to the study of orthogonal polynomials related to Sobolev inner products which are defined in terms of divided-difference operators having the fundamental property of leaving a polynomial of degree $n-1$ when applied to a polynomial of degree $n$. This paper gives analytic properties for the orthogonal polynomials, including the second order holonomic difference equation satisfied by them.

2022-05Journal article

Open access

Classification of Laguerre-Hahn orthogonal polynomials of class one

Publication . Rebocho, M. N.; Filipuk, Galina

We study orthogonal polynomials related to Stieltjes functions satisfying Riccati type differential equations with polynomial coefficients, AS0 = BS2 + CS + D, with max {deg(A); deg(B)} <= 3; deg(C) <= 2. We derive recurrences for the three-term recurrence relation coefficients of the orthogonal polynomials, including connections with some forms of discrete Painlevé equations.

2019Preprint

Open access