Discrete semiclassical orthogonal polynomials of class one

Diego Dominici and Francisco Marcellán

Vol. 268 (2014), No. 2, 389–411

DOI: 10.2140/pjm.2014.268.389

Abstract

We study discrete semiclassical orthogonal polynomials of class $s=1$. By considering particular solutions of the Pearson equation, we obtain five canonical families of such polynomials. We also consider limit relations between these and other families of orthogonal polynomials.

Keywords

discrete orthogonal polynomials, Pearson equation, discrete semiclassical polynomials, Laguerre–Freud equations, Painlevé equations

Mathematical Subject Classification 2010

Primary: 33C47

Secondary: 34M55, 33E17, 42C05

Milestones

Received: 8 November 2012

Revised: 16 January 2014

Accepted: 7 February 2014

Published: 21 June 2014