On Obtaining Dual Sequences Via Quasi-Monomiality

Abstract

Abstract In this paper, we introduce a method to obtain the dual sequence of a given polynomial set using the lowering operator associated with the involved polynomials. As application, we derive polynomial expansions of analytic functions. The particular case corresponding to Boas–Buck polynomials allows us to unify many polynomial expansions of analytic functions in the literature. This method can be useful in studying many problems arising in the theory of polynomials as the so-called connection and linearization problems.