Laguerre, Hermite and Meixner polynomials arising from polynomials in several variables

Abstract

Among polynomials in several variables of given form, the Laguerre and Hermite polynomials are recovered. This is obtained by requiring that the polynomials in several variables satisfy known properties characterizing the classical polynomials. Analogous characterizations of the Meixner polynomials are likewise determined. These are based on the characteristic properties of the Meixner polynomials recently established. All new properties generalize the previous ones.