The hankel transform of generalized bell numbers and its q-analogue

Abstract

In this paper, a kind of recurrence relation for the generalized Bell numbers is established which is used to obtain the Hankel transform of generalized Bell numbers. Moreover, a q-analogue of generalized Bell numbers is defined and some necessary properties are obtained including a recurrence relation, which plays an important role in formulating a possible solution to determine the Hankel transform of the q-analogue.