Degenerate central Bell numbers and polynomials

Abstract

Here we study the degenerate central Bell numbers and polynomials as a degenerate version of the recently introduced central Bell numbers and polynomials, which are motivated by Zhang’s work ‘Some identities involving the Euler and the central factorial numbers’ (Zhang in Fibonacci Quart 36(2):154–157, 1998) and we derive some properties, identities, and recurrence relations for these numbers and polynomials. In particular, we find various expressions for the degenerate central Bell numbers and polynomials.