Exceptional Meixner and Laguerre orthogonal polynomials

Using Casorati determinants of Meixner polynomials (m n )n , we construct for each pair F = (F1, F2) of finite sets of positive integers a sequence of polynomials ma,c;F n , n ∈ σF , which are eigenfunctions of a second order difference operator, where σF is certain infinite set of nonnegative integers, σF N. When c and F satisfy a suitable admissibility condition, we prove that the polynomials ma,c;F n , n ∈ σF , are actually exceptional Meixner polynomials; that is, in addition, they are orthogonal and complete with respect to a positive measure. By passing to the limit, we transform the Casorati determinant of Meixner polynomials into a Wronskian type determinant of Laguerre polynomials (Ln )n . Under the admissibility conditions for F and α, these Wronskian type determinants turn out to be exceptional Laguerre polynomials. c ⃝ 2014 Elsevier Inc. All rights reserved.