Asymptotic analysis of a family of Sobolev orthogonal polynomials related to the generalized Charlier polynomials

Abstract

In this paper we tackle the asymptotic behavior of a family of orthogonal polynomials with respect to a nonstandard inner product involving the forward operator Δ. Concretely, we treat the generalized Charlier weights in the framework of Δ--Sobolev orthogonality. We obtain an asymptotic expansion for this orthogonal polynomials where the falling factorial polynomials play an important role.

18 pages. This version corresponds to the version published in the Journal of Approximation Theory where some minor errors in Theorem 15 are corrected