Admissibility condition for exceptional Laguerre polynomials

TL;DR

This paper establishes a precise criterion for the integrability of weights in exceptional Laguerre polynomials, linking it to the absence of singularities in the related differential operator within the positive real axis.

Contribution

It provides a necessary and sufficient condition for weight integrability, clarifying the role of singularities in the differential operator for exceptional Laguerre polynomials.

Findings

Derived a condition for weight integrability

Connected integrability to singularity absence in differential operator

Enhanced understanding of exceptional Laguerre polynomial properties

Abstract

We prove a necessary and sufficient condition for the integrability of the weight associated to the exceptional Laguerre polynomials. This condition is very much related to the fact that the associated second order differential operator has no singularities in $(0,+\infty)$.