Discrete semiclassical orthogonal polynomials of class one

TL;DR

This paper classifies and analyzes five canonical families of discrete semiclassical orthogonal polynomials of class one, exploring their interrelations and limit behaviors.

Contribution

It provides a complete classification of discrete semiclassical orthogonal polynomials of class one and examines their limit relations with other polynomial families.

Findings

Identified five canonical families of these polynomials.

Established limit relations between these families and others.

Provided a comprehensive framework for understanding their interconnections.

Abstract

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