A polynomial set is called quasi-monomial if and only if it is possible to define two operators and , independent of , such that
In this paper, the author shows that every polynomial set is quasi-monomial and presents some useful tools to explicitly express the operators and for some polynomial families given by their generating functions. The obtained results are then applied to the Boas-Buck polynomial sets. Some closely-related earlier works include (among others cited by the author) a recent paper by G. Dattoli, the reviewer and C. Cesarano [Appl. Math. Comput. 124, No. 1, 117–127 (2001; Zbl 1036.33008)].