The q-Racah-Krall-type polynomials

TL;DR

This paper introduces a new class of Krall-type polynomials derived from q-Racah polynomials by adding mass points, exploring their algebraic properties and limit cases.

Contribution

It presents the construction and analysis of q-Racah-Krall-type polynomials with added mass points, expanding the family of orthogonal polynomials.

Findings

Derived algebraic properties of q-Racah-Krall polynomials

Identified limit cases of the polynomials

Extended the theory of orthogonal polynomials with mass points

Abstract

In this paper the Krall-type polynomials obtained via the addition of two mass points to the weight function of the \textit{standard} $q$-Racah polynomials are introduced. Several algebraic properties of these polynomials are obtained and some of their limit cases are discussed.