Extended central factorial polynomials of the second kind

Taekyun Kim,Gwan-Woo Jang,Jongkyum Kwon,Dae San Kim

doi:10.1186/s13662-019-1963-1

Taekyun Kim, Gwan-Woo Jang + Show 2 more

Open Access

https://doi.org/10.1186/s13662-019-1963-1

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Abstract

In this paper, we consider the extended central factorial polynomials and numbers of the second kind, and investigate some properties and identities for these polynomials and numbers. In addition, we give some relations between those polynomials and the extended central Bell polynomials. Finally, we present some applications of our results to moments of Poisson distributions.

Highlights

For n ≥ 0, the central factorial numbers of the second kind are defined by n xn = T(n, k)x[k], n ≥ 0, k=0 (1.1) where x[k] = x(x + k 2 1)(x 2) · · · (x 1), k ≥
1 Introduction For n ≥ 0, the central factorial numbers of the second kind are defined by n xn = T(n, k)x[k], n ≥ 0, k=0 (1.1)
We give some relations between those polynomials and the extended central Bell polynomials

Summary

Introduction

When x = 0, S2,r(n, k) = S2,r(n, k|0), n, k ≥ 0, are called the extended Stirling numbers of the second kind. When x = 0, T(r)(n, k) = T(r)(n, k|0), n, k ≥ 0, are called the extended central factorial numbers of the second kind. By combining (2.4)–(2.6), we obtain the following theorem. By (2.27) and (2.32), we obtain the following theorem. T(l, m)T(n – l, k), m l l=m where n, m, k ≥ 0 with n ≥ m + k

Application

Conclusions