Associated with each complex-valued random variable satisfying appropriate integrability
conditions, we introduce a different generalization of the Stirling numbers of the second kind …

We introduce probabilistic Stirling numbers of the first kind s Y (n, k) associated with a
complex-valued random variable Y satisfying appropriate integrability conditions, thus …

Associated to each random variable Y satisfying appropriate moment conditions, we
introduce a different generalization of the Stirling numbers of the second kind. Some …

We give explicit estimates for the Stirling numbers of the second kind $ S (n, m) $. With a few
exceptions, such estimates are asymptotically sharp. The form of these estimates varies …

In this paper, we introduce the r-central factorial numbers with even indices of the first and
second kind as extended versions of the central factorial numbers with even indices of both …

We give explicit upper bounds for the Stirling numbers of the first kind s (n, m) which are
asymptotically sharp. The form of such bounds varies according to m lying in the central or …

The Jacobi-Stirling numbers of the first and second kind were introduced in 2007 by Everitt
et al. In this article we find new explicit formulas for Jacobi Stirling numbers. Furthermore, we …

In this paper, we first focus on the sum of powers of the first n positive odd integers, T k (n)= 1
k+ 3 k+ 5 k+⋯+(2 n− 1) k, and derive in an elementary way a polynomial formula for T k (n) in …

We defie the (𝑞, ᾱ)-Whitney numbers which are reduced to the ᾱ-Whitney numbers when
𝑞→ 1. Moreover, we obtain several properties of these numbers such as explicit formulas …

We give explicit upper and lower bounds for a large subset of Comtet numbers s α (n, m) of
the first kind, including the r-Stirling numbers of the first kind, among others. In many …