Generalized Central Factorial Numbers with Odd Arguments

The aim of this paper is to give some new identities and relations related to the some families of special numbers such as the Bernoulli numbers, the Euler numbers, the Stirling numbers of the first and second kinds, the central factorial numbers and also the numbers y1(n,k,?) and y2(n,k,?) which are given Simsek [31]. Our method is related to the functional equations of the generating functions and the fermionic and bosonic p-adic Volkenborn integral on Zp. Finally, we give remarks and comments on our results.

Download Full-text

On Central Complete and Incomplete Bell Polynomials I

Symmetry ◽

10.3390/sym11020288 ◽

2019 ◽

Vol 11 (2) ◽

pp. 288 ◽

Cited By ~ 6

Author(s):

Taekyun Kim ◽

Dae Kim ◽

Gwan-Woo Jang

Keyword(s):

Bell Polynomials ◽

Explicit Formulas ◽

Central Factorial Numbers

In this paper, we introduce central complete and incomplete Bell polynomials which can be viewed as generalizations of central Bell polynomials and central factorial numbers of the second kind, and also as ’central’ analogues for complete and incomplete Bell polynomials. Further, some properties and identities for these polynomials are investigated. In particular, we provide explicit formulas for the central complete and incomplete Bell polynomials related to central factorial numbers of the second kind.

Download Full-text

The $D$ numbers and the central factorial numbers

Publicationes Mathematicae Debrecen ◽

10.5486/pmd.2011.4917 ◽

2011 ◽

Vol 79 (1-2) ◽

pp. 41-53 ◽

Cited By ~ 2

Author(s):

GUODONG LIU

Keyword(s):

Central Factorial Numbers ◽

D Numbers

Download Full-text

On r-Central Incomplete and Complete Bell Polynomials

Symmetry ◽

10.3390/sym11050724 ◽

2019 ◽

Vol 11 (5) ◽

pp. 724 ◽

Cited By ~ 1

Author(s):

Dae San Kim ◽

Han Young Kim ◽

Dojin Kim ◽

Taekyun Kim

Keyword(s):

Stirling Numbers ◽

Bell Polynomials ◽

Explicit Formulas ◽

Central Factorial Numbers

Here we would like to introduce the extended r-central incomplete and complete Bell polynomials, as multivariate versions of the recently studied extended r-central factorial numbers of the second kind and the extended r-central Bell polynomials, and also as multivariate versions of the r- Stirling numbers of the second kind and the extended r-Bell polynomials. In this paper, we study several properties, some identities and various explicit formulas about these polynomials and their connections as well.

Download Full-text

Some Computational Formulas forD-Nörlund Numbers

Abstract and Applied Analysis ◽

10.1155/2009/430452 ◽

2009 ◽

Vol 2009 ◽

pp. 1-7 ◽

Cited By ~ 1

Author(s):

Guodong Liu

Keyword(s):

Generating Function ◽

Bernoulli Numbers ◽

Central Factorial Numbers

The author establishes some identities involving theDnumbers, Bernoulli numbers, and central factorial numbers of the first kind. A generating function and several computational formulas forD-Nörlund numbers are also presented.

Download Full-text

A Combinatorial Approach to the Generalized Central Factorial Numbers

Mediterranean Journal of Mathematics ◽

10.1007/s00009-021-01830-5 ◽

2021 ◽

Vol 18 (5) ◽

Author(s):

Takao Komatsu ◽

José L. Ramírez ◽

Diego Villamizar

Keyword(s):

Combinatorial Approach ◽

Central Factorial Numbers

Download Full-text

On degenerate central complete bell polynomials

Applicable Analysis and Discrete Mathematics ◽

10.2298/aadm181103034k ◽

2019 ◽

Vol 13 (3) ◽

pp. 805-818

Author(s):

Taekyun Kim ◽

San Kim ◽

Gwan-Woo Jang

Keyword(s):

Bell Polynomials ◽

Explicit Formulas ◽

Central Factorial Numbers

In this paper, we consider of generalized central complete and incomplete Bell polynomials called degenerate central complete and incomplete Bell polynomials. These polynomials are generalizations of the recently introduced central complete Bell polynomials and `degenerate' analogues for the central complete and incomplete Bell polynomials. We investigate some properties and identities for these polynomials. Especially, we give explicit formulas for the degenerate central complete and incomplete Bell polynomials related to degenerate central factorial numbers of the second kind.

Download Full-text