Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters

TL;DR

This paper introduces new families of exceptional Hahn and Jacobi polynomials that depend on an arbitrary number of continuous parameters, expanding the class of orthogonal polynomials with gaps in their degrees.

Contribution

The authors construct novel exceptional Hahn and Jacobi polynomials with multiple continuous parameters, broadening the scope of orthogonal polynomial families.

Findings

New exceptional Hahn and Jacobi polynomials constructed

Polynomials depend on an arbitrary number of continuous parameters

Polynomials are eigenfunctions of second order difference or differential operators

Abstract

We construct new examples of exceptional Hahn and Jacobi polynomials. Exceptional polynomials are orthogonal polynomials with respect to a measure which are also eigenfunctions of a second order difference or differential operator. The most apparent difference between classical or classical discrete orthogonal polynomials and their exceptional counterparts is that the exceptional families have gaps in their degrees, in the sense that not all degrees are present in the sequence of polynomials. The new examples have the novelty that they depend on an arbitrary number of continuous parameters.