From Krall discrete orthogonal polynomials to Krall polynomials

TL;DR

This paper explores a novel limiting process to derive Krall polynomials from Krall discrete polynomials, highlighting differences from the classical Askey scheme methods.

Contribution

It introduces a new limiting procedure for Krall polynomials that differs from the standard approach used for classical polynomials.

Findings

New limiting procedure for Krall polynomials

Distinct approach from classical Askey scheme

Enhanced understanding of polynomial relationships

Abstract

We show how to get Krall polynomials from Krall discrete polynomials using a procedure of passing to the limit in some of the parameters of the family. We also show that this procedure has to be different to the standard one used in the Askey scheme to go from the classical discrete polynomials to the classical polynomials.