We prove that every rational extension of the quantum harmonic oscillator that is exactly
solvable by polynomials is monodromy free, and therefore can be obtained by applying a …

It was recently conjectured that every system of exceptional orthogonal polynomials is
related to a classical orthogonal polynomial system by a sequence of Darboux …

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 …

We study the zeros of exceptional Hermite polynomials associated with an even partition λ.
We prove several conjectures regarding the asymptotic behaviour of both the regular (real) …

A comprehensive review of exactly solvable quantum mechanics is presented with the
emphasis of the recently discovered multi-indexed orthogonal polynomials. The main …

The aim of this paper is to present the construction of exceptional Laguerre polynomials in a
systematic way and to provide new asymptotic results on the location of the zeros. To …

We derive identities between determinants whose entries are Hermite polynomials. These
identities have a combinatorial interpretation in terms of Maya diagrams, partitions and …

The work of Adler provides necessary and sufficient conditions for the Wronskian of a given
sequence of eigenfunctions of Schrödinger's equation to have constant sign in its domain of …

In a previous paper we derived equivalence relations for pseudo-Wronskian determinants of
Hermite polynomials. In this paper we obtain the analogous result for Laguerre and Jacobi …

Exceptional orthogonal polynomials are families of orthogonal polynomials that arise as
solutions of Sturm-Liouville eigenvalue problems. They generalize the classical families of …