Differential orthogonality: Laguerre and Hermite cases with applications

Abstract

Let mu be a finite positive Borel measure supported on R, L[f] = xf ''+ (alpha +1 - x)f'with alpha > -1, or L[f] = 1/2f ''- xf', and m a natural number. We study algebraic, analytic and asymptotic properties of the sequence of monic polynomials {Q(n)}(n>m) that satisfy the orthogonality relationsintegral L[Q(n)](x)x(k)d mu(x) = 0 for all 0 <= k <= n - 1.We also provide a fluid dynamics model for the zeros of these polynomials. (C) 2015 Elsevier Inc. All rights reserved.