Functions and Jordan canonical forms of Riordan matrices

This paper collects results about Riordan arrays in the framework of matrix functions; actually, the following methodology applies to any square matrix m x m with exactly one eigen-value lambda of algebraic multiplicity m is an element of N. Generalized Lagrange bases are used to construct Hermite polynomials that interpolate a family of functions; moreover, we show a parallel application of such functions via Jordan canonical forms and case studies are given. (C) 2018 Elsevier Inc. All rights reserved.