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 times m with exactly one eigenvalue λ of algebraic multiplicity m. 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.