English
Related papers

Related papers: On central complete Bell polynomials

200 papers

In this paper, we study the degenerate central complete and incomplete Bell polynomials which are degenerate versions of the recently introduced central complete and incomplete Bell polynomials and also central analogues for the degenerate…

Number Theory · Mathematics 2019-02-22 Taekyun Kim , Dae San Kim , Gwan-Woo Jang

In this paper, we introduce the extended r-central factorial numbers of the second and first kinds and the extended r-central Bell polynomials, as extended versions and central analogues of some previously introduced numbers and…

Number Theory · Mathematics 2019-03-29 Dae San Kim , Dmitry V. Dolgy , Dojin Kim , Taekyun Kim

The aim of this paper is to introduce Bell polynomials and numbers of the second kind and poly-Bell polynomials and numbers of the second kind, and to derive their explicit expressions, recurrence relations and some identities involving…

Number Theory · Mathematics 2021-06-29 Dae San Kim , Dmitry V. Dolgy , Hye-Kyung Kim , Hyunseok Lee , Taekyun Kim

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. In this paper, we study the probabilistic central Bell polynomials associated with random variable Y, as probabilistic extension of the…

Number Theory · Mathematics 2024-03-04 R. Xu , Y. Ma , T. Kim , D. S. Kim , S. Boulaars

In this paper, we introduce the degenerate central factorial polynomials and numbers of the second kind which are degenerate versions of the central factorial polynomials and numbers of the second kind. We derive some properties and…

Number Theory · Mathematics 2019-02-13 Taekyun Kim , Dae san Kim

The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of…

Number Theory · Mathematics 2009-11-17 Boris Y. Rubinstein

In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also…

Classical Analysis and ODEs · Mathematics 2010-02-06 Donal F. Connon

In the paper, in light of the generating function of the complete Bell polynomials and other techniques, the author presents concise and elegant proofs of three formulas for the complete Bell polynomials.

Combinatorics · Mathematics 2026-05-25 Feng Qi

Our paper deals about identities involving Bell polynomials. Some identities on Bell polynomials derived using generating function and successive derivatives of binomial type sequences. We give some relations between Bell polynomials and…

Combinatorics · Mathematics 2008-06-24 Miloud Mihoubi

The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate version of the Bell numbers and polynomials. we derive some new identities and properties of those numbers and polynomials that are…

Number Theory · Mathematics 2021-08-16 Taekyun Kim , Dae San Kim , Hyunseok Lee , Seongho Park

Recently, several authors have studied the degenerate Bernoulli and Euler polynomials and given some intersting identities of those polynomials. In this paper, we consider the degenerate Bell numbers and polynomials and derive some new…

Number Theory · Mathematics 2015-07-09 Taekyun Kim , Dae san Kim

In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and investigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate…

Number Theory · Mathematics 2015-05-27 Dae San Kim , Taekyun Kim

Departing from a class of infinite series with central binomial coefficients in the numerator and depending on a positive integer parameter, we first extend known identities to all complex parameters. Then we use various methods, including…

Number Theory · Mathematics 2025-11-04 Karl Dilcher , Christophe Vignat

Many important special numbers appear in the expansions of some polynomials in terms of central factorials and vice versa, for example central factorial numbers, degenerate central factorial numbers, and central Lah numbers which are…

Number Theory · Mathematics 2023-05-24 Dae san Kim , Taekyun Kim

New methods for derivation of Bell polynomials of the second kind are presented. The methods are based on an ordinary generating function and its composita. The relation between a composita and a Bell polynomial is demonstrated. Main…

Combinatorics · Mathematics 2011-09-09 Vladimir Kruchinin

This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.

Classical Analysis and ODEs · Mathematics 2016-10-10 Khristo N. Boyadzhiev

Recently, Kim-Kim introduced the lambda-umbral calculus, in which the lambda-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and investigate…

Number Theory · Mathematics 2023-01-11 Yuankui Ma , Taekyun Kim , Hyunseok Lee , Dae San Kim

This paper aims to construct a new family of numbers and polynomials which are related to the Bell numbers and polynomials by means of the confluent hypergeometric function. We give various properties of these numbers and polynomials…

Number Theory · Mathematics 2018-12-12 Ghania Guettai , Diffalah Laissaoui , Mourad Rahmani , Madjid Sebaoui

We derive an expression for the generalized Bernoulli numbers in terms of the Bernoulli numbers involving the (exponential) complete Bell polynomials.

Classical Analysis and ODEs · Mathematics 2018-01-25 Donal F. Connon

We prove an inverse relation and a family of convolution formulas involving partial Bell polynomials. Known and some presumably new combinatorial identities of convolution type are discussed. Our approach relies on an interesting…

Combinatorics · Mathematics 2013-07-23 Daniel Birmajer , Juan B. Gil , Michael D. Weiner
‹ Prev 1 2 3 10 Next ›