Behavior of zeros of $X_1$-Jacobi and $X_1$-Laguerre exceptional polynomials

Abstract

The $X_1$-Jacobi and the $X_1$-Laguerre exceptional orthogonal polynomials have been introduced and studied by Gómez-Ullate, Kamran and Milson in a series of papers. In this note, we establish some properties, such as interlacing, monotonicity with respect to the parameters and order, about the so-called \textit{regular} and \textit{exceptional} zeros of these two classes of polynomials.