Exceptional Meixner and Laguerre orthogonal polynomials

Using Casorati determinants of Meixner polynomials (m(n)(a,c))(n), we construct for each pair F = (F-1, F-2) of finite sets of positive integers a sequence of polynomials m(n)(a,c;F), n is an element of sigma(F), which are eigenfunctions of a second order difference operator, where sigma(F) is certain infinite set of normegative integers, sigma(F) not subset of N. When c and F satisfy a suitable admissibility condition, we prove that the polynomials m(n)(a,c;F), n is an element of sigma(F), 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 (L-n(alpha))(n). Under the admissibility conditions for F and alpha, these Wronskian type determinants turn out to be exceptional Laguerre polynomials. (C) 2014 Elsevier Inc. All rights reserved.