Poly-central factorial sequences and poly-central-Bell polynomials

Hye Kyung Kim,Taekyun Kim

doi:10.1186/s13662-021-03663-8

Abstract

In this paper, we introduce poly-central factorial sequences and poly-central Bell polynomials arising from the polyexponential functions, reducing them to central factorials and central Bell polynomials of the second kind respectively when k = 1. We also show some relations: between poly-central factorial sequences and power of x; between poly-central Bell polynomials and power of x; between poly-central Bell polynomials and the poly-Bell polynomials; between poly-central Bell polynomials and higher order type 2 Bernoulli polynomials of second kind; recurrence formula of poly-central Bell polynomials.

Highlights

1 Introduction The central factorial numbers of the first and second kinds consist of the same kind of reciprocity as the corresponding polynomials for the Stirling numbers of the first and second kinds [20]
We introduce poly-central factorial sequences and poly-central Bell polynomials arising from the polyexponential functions, reducing them to central factorials and central Bell polynomials of the second kind respectively when k = 1
We show some relations: between poly-central factorial sequences and power of x; between poly-central Bell polynomials and power of x; between poly-central Bell polynomials and the poly-Bell polynomials; between poly-central Bell polynomials and higher order type 2 Bernoulli polynomials of second kind; recurrence formula of poly-central Bell polynomials

Summary

Introduction

The central factorial numbers of the first and second kinds consist of the same kind of reciprocity as the corresponding polynomials for the Stirling numbers of the first and second kinds [20]. We introduce poly-central factorial sequences and poly-central Bell polynomials arising from the polyexponential functions, reducing them to central factorials and central Bell polynomials of the second kind respectively when k = 1. From (4) and (5), the central factorial numbers of the second kind are given by t e2 Kim and Kim introduced the central Bell polynomials B(nc)(x) defined by n

Results

Conclusion