Limit relations between $q$-Krall type orthogonal polynomials

TL;DR

This paper investigates the limit relations among various $q$-Krall type orthogonal polynomials, extending classical results by modifying linear functionals with added mass points and analyzing their asymptotic behaviors.

Contribution

It introduces a new modification of $q$-classical functionals with mass points and establishes limit relations among different $q$-Krall polynomial families.

Findings

Established limit relations between $q$-Krall modifications of classical families.

Extended classical results to include modifications with added mass points.

Provided a framework for understanding asymptotic behaviors of these polynomials.

Abstract

In this paper, we consider a natural extension of several results related to Krall-type polynomials introducing a modification of a $q$-classical linear functional via the addition of one or two mass points. The limit relations between the $q$-Krall type modification of big $q$-Jacobi, little $q$-Jacobi, big $q$-Laguerre, and other families of the $q$-Hahn tableau are established.