Exceptional Jacobi polynomials

TL;DR

This paper introduces a systematic partition-based framework for describing exceptional Jacobi polynomials, providing new constructions and asymptotic analysis of their zeros.

Contribution

It presents a novel partition-based labeling method and proves asymptotic properties of the zeros of exceptional Jacobi polynomials.

Findings

Partition labeling simplifies the description of exceptional Jacobi polynomials

Asymptotic results characterize the behavior of regular and exceptional zeros

The framework enhances understanding of polynomial structure and zero distribution

Abstract

In this paper we present a systematic way to describe exceptional Jacobi polynomials via two partitions. We give the construction of these polynomials and restate the known aspects of these polynomials in terms of their partitions. The aim is to show that the use of partitions is an elegant way to label these polynomials. Moreover, we prove asymptotic results according to the regular and exceptional zeros of these polynomials.