1 Discrete q-Hermite polynomials: An elementary approach

We present a simple approach to discrete q Hermite polynomials with special emphasis on analogies with the classical case. The so-called “discrete q Hermite polynomials ” are q analogues of the classical Hermite polynomials which generalize most of their elementary properties. The purpose of this paper is to emphasize these analogies without recourse to sophisticated general theories. Some 35 years ago I stumbled upon these polynomials (cf. [3], [4]) as I studied some q identities from the point of view o