Some results on quasi-monomiality

摘要

A polynomial set {Pn}n⩾0 is called quasi-monomial if and only if it is possible to define two operators P and M, independent of n, such thatP(Pn)(x)=nPn−1(x)andM(Pn)(x)=Pn+1(x)In this paper, we show that every polynomial set is quasi-monomial and we present some useful tools to explicitly express the P and M operators for some polynomial families given by their generating functions. The obtained results are applied to Boas–Buck polynomial sets.