There are a number of intriguing connections between Painlevé equations and orthogonal
polynomials, and this book is one of the first to provide an introduction to these. Researchers …

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

Abstract Using Casorati determinants of Meixner polynomials (mna, c) n, we construct for
each pair F=(F 1, F 2) of finite sets of positive integers a sequence of polynomials mna, c; F …

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 …

Considering successive extensions of primary translationally shape invariant potentials, we
enlarge the Krein-Adler theorem to mixed chains of state adding and state-deleting Darboux …

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

The bispectral anti-isomorphism is applied to differential operators involving elements of the
stabilizer ring to produce explicit formulas for all difference operators having any of the …

Abstract Using Casorati determinants of Charlier polynomials (cna) n, we construct for each
finite set F of positive integers a sequence of polynomials cn F, n∈ σ F, which are …

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) …

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 …