English
Related papers

Related papers: A note on degenerate Bell numbers and polynomials

200 papers

Recently, degenerate Cauchy numbers and polynomials are introduced in [10]. In this paper, we study the degenerate Cauchy numbers and polynomials which are different from the previous degenerate Cauchy numbers and polynomials. In addition,…

Number Theory · Mathematics 2017-08-25 T. Kim

Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek's recent work 'Generating functions for unification of the multidimensional Bernstein polynomials and…

Number Theory · Mathematics 2018-06-19 Taekyun Kim , 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

In this paper, we consider the problem of representing any polynomial in terms of the ordered Bell and degenerate ordered Bell polynomials, and more generally of the higher-order ordered Bell and higher-order degenerate ordered Bell…

Number Theory · Mathematics 2021-10-08 Dae san Kim , Taekyun Kim

Recently, Masjed-Jamei-Beyki-Koepf studied the so called new type Euler polynomials without making use of Euler polynomials of complex variable. Here we study degenerate and type 2 versions of these new type Euler polynomials, namely the…

Number Theory · Mathematics 2019-08-30 Taekyun Kim , Dae san Kim , Lee-Chae Jang , Han-Young Kim

In this paper, we introduce two variable degenerate Bell polynomials as a generalization of the degenerate Bell polynomials which were studied earlier. Among other things, we show their connections with Poisson degenerate central moments…

Number Theory · Mathematics 2020-06-25 Dae San Kim , Taekyun Kim , Han-Young Kim , Hynseok Lee

Recently, Bovadzhiev studied a power series whose coefficients are binomial expressions and extended some known formulas involving classical special functions and polynomials. The aim of this paper is to adopt his ideas to express several…

Number Theory · Mathematics 2021-12-17 Taekyun Kim , Dae San Kim

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study the probabilistic degenerate poly-Bell polynomials associated with the random variable Y, arising from the…

Number Theory · Mathematics 2025-03-11 Pengxiang Xue , Yuankui Ma , Taekyun Kim , Dae San Kim , Wenpeng Zhang

The main aim of this paper is to define and investigate a new class of the degenerate poly-Frobenius-Genocchi polynomials with the help of the polyexponential functions. In this paper, we define the degenerate poly-Frobenius-Genocchi…

Number Theory · Mathematics 2020-07-17 Burak Kurt

We introduce the degenerate Bernoulli numbers of the second kind as a degenerate version of the Bernoulli numbers of the second kind. We derive a family of nonlinear differential equations satisfied by a function closely related to the…

Number Theory · Mathematics 2018-04-27 Taekyun Kim , Dae San Kim

In this paper, we introduce the Lah-Bell numbers and their natural extensions, namely the Lah-Bell polynomials, and derive some basic properties of such numbers and polynomials by using elementary methods. In addition, we consider the…

Number Theory · Mathematics 2020-07-28 Dae San Kim , Taekyun Kim

In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…

Number Theory · Mathematics 2021-04-20 Nabiullah Khan , Saddam Husain

In recent years, some degenerate versions of quite a few special numbers and polynomials are introduced and investigated by means of various methods. The aim of this paper is to study some results on degenerate harmonic numbers, degenerate…

Number Theory · Mathematics 2022-08-30 Taekyun Kim , Dae San Kim

In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials and more generally of the higher-order degenerate Bernoulli polynomials. We derive explicit formulas with the help of…

Number Theory · Mathematics 2021-08-12 Dae san Kim , Taekyun Kim

In a previous paper, Rahmani introduced a new family of p-Bernoulli numbers and polynomials by means of the Gauss hypergeometric function. Motivated by this paper and as a degenerate version of those numbers and polynomials, we introduce…

Number Theory · Mathematics 2021-01-07 Taekyun Kim , Dae san Kim , Lee-Chae jang , Hyunseok Lee , Hanyoung Kim

In this paper, we consider the degenerate Changhee numbers and polynomials of the second kind which are different from the previously introduced degenerate Changhee numbers and polynomials by Kwon-Kim-Seo (see [11]). We investigate some…

Number Theory · Mathematics 2017-08-01 Taekyun Kim , Dae San Kim

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

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

Following Spivey's pivotal discovery of a recurrence relation for Bell numbers, significant research has emerged concerning various generalizations of Bell numbers and polynomials. For example, Kim and Kim established a Spivey-type…

Number Theory · Mathematics 2025-08-26 Taekyun Kim , Dae San Kim

This paper addresses the unnatural appearance of the two-variable degenerate Fubini polynomials in a recently derived Spivey-type recurrence relation for the fully degenerate Bell polynomials. To solve this, we introduce a new family of…

Combinatorics · Mathematics 2025-11-18 Taekyun Kim , Dae San Kim