The limit of the differences of the generalized factorial, its q- and p, q- analogue

Abstract

The limit of the differences of the generalized factorial, denoted by F_α,γ(n,k), was discussed extensively in [13]. It has been observed in [13] that F_α,γ(n,A:) is a kind of a generalization of the Stirling numbers of the first kind. In this paper, a q-, and a p,q-analogue of F_α,γ(n, k) will be established and some of their necessary properties will be given. Moreover, the p, q-analogue of F_α,γ(n, k) will be discussed in the context of 0-1 tableaux.