Exceptional Meixner and Laguerre orthogonal polynomials

Using Casorati determinants of Meixner polynomials (mna,c)n, we construct for each pair F=(F1,F2) of finite sets of positive integers a sequence of polynomials mna,c;F, 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 mna,c;F, 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 (Lnα)n. Under the admissibility conditions for F and α, these Wronskian type determinants turn out to be exceptional Laguerre polynomials.