The Electrostatic Properties of Zeros of Exceptional Laguerre and Jacobi Polynomials and stable interpolation

TL;DR

This paper investigates the electrostatic properties of zeros of exceptional Laguerre and Jacobi polynomials, linking these properties to interpolation stability and analyzing energy limits of the zeros.

Contribution

It introduces a detailed analysis of electrostatic properties of zeros of exceptional polynomials and connects these to interpolation stability and energy limits.

Findings

Electrostatic properties of zeros are characterized.

A stability result for interpolation systems is derived.

Limits of energy for regular zeros are analyzed.

Abstract

We will examine the electrostatic properties of exceptional and regular zeros of $X_m$-Laguerre and $X_m$-Jacobi polynomials. Since there is a close connection between the electrostatic properties of the zeros and the stability of interpolation on the system of zeros, we can deduce an Egerv\'ary-Tur\' an type result as well. The limit of the energy on the regular zeros are also investigated.