Some Appell-type orthogonal polynomials on lattices

Abstract

We investigate on some Appel-type orthogonal polynomial sequences on q-quadratic lattices and we provide some entire new characterizations of the Al-Salam-Chihara polynomials (including the Rogers q-Hermite polynomials). The corresponding forms are well described.

On Another Characterization of Askey-Wilson Polynomials

“…For our second structure relation mentioned at the end of the introduction, the following result follows. We emphasize that this result is new and generalizes a recent result available in [14]. Theorem 3.2.…”