On three-dimensional q -riordan arrays

Abstract

In this article, we define three-dimensional q-Riordan arrays and q-Riordan representations for these arrays. Also, we give four cases of infinite multiplication three-dimensional matrices of these arrays. As applications, we obtain three-dimensional q-Pascal-like matrix and its inverse matrix by Heine's binomial formula, using combinatorial identities. Finally, we consider the generalization of three-dimensional q-Pascal-like matrix and give some identities involving q-binomial coefficients.