Beyond the Monomiality: the Monumbrality Principle.

The monomiality principle has allowed the derivation, in a fairly straightforward way, of the properties of many families of special polynomials, recognized as quasi monomials. The family of quasimonomials is large, but not all the special polynomials can be framed within this category. In this paper we will prove the existence of a larger family, including the quasi-monomials, by taking advantage from the umbral calculus and by introducing the concept of monumbrality, which appears very useful to get a deeper understanding in the nature and role of special polynomials. [ABSTRACT FROM AUTHOR]