English
Related papers

Related papers: A note on degenerate Bell numbers and polynomials

200 papers

In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were recently introduced by Jang et. al. We derive their explicit expressions and some…

Number Theory · Mathematics 2020-04-21 Taekyun Kim , Dae San Kim , Han Young Kim , Jongkyum Kwon

We introduce degenerate Hermite polynomials as a degenerate version of the ordinary Hermite polynomials. Then, among other things, by using the formula about representing one lambda-Sheffer polynomial in terms of other lambda-Sheffer…

Number Theory · Mathematics 2020-10-29 Taekyun Kim , Dae San Kim , Lee-Chae Jang , Hyunseok Lee , Hanyoung Kim

The foremost aim of this study is to introduce and study several combinatorial properties and highlight specific aspects of a new class of polynomials sequences known as degenerate Krawtchouk Appell polynomials associated with the…

Combinatorics · Mathematics 2026-05-19 Mohamed Abdelkader , Mohamed Rhaima

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

In this paper, we investigate some properties and identities for degenerate Euler polynomials in connection with degenerate Bernstein polynomials by means of fermionic p-adic integrals on Zp and generating functions. In addition, we study…

Number Theory · Mathematics 2019-04-19 Won Joo Kim , Dae San Kim , Han Young Kim , Taekyun Kim

This paper introduces a degenerate version of the Euler-Seidel method by incorporating a parameter lambda into the classical recurrence relation. We define a degenerate Euler-Seidel matrix associated with an initial sequence and establish…

Number Theory · Mathematics 2025-12-24 Taekyun Kim , Dae San Kim , Hyunseok Lee , Kyo-Shin Hwang

Spivey found a recurrence relation for the Bell numbers by using combinatorial method. The aim of this paper is to derive Spivey's type recurrence relations for the degenerate Bell polynomials and the degenerate Dowling polynomials by using…

Number Theory · Mathematics 2025-03-05 Taekyun Kim , Dae San Kim

In this paper, we study a class of sequences of polynomials linked to the sequence of Bell polynomials. Some sequences of this class have applications on the theory of hyperbolic differential equations and other sequences generalize…

Combinatorics · Mathematics 2023-11-20 Miloud Mihoubi , Madjid Sahari

We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain…

Rings and Algebras · Mathematics 2014-03-06 Paweł J. Szabłowski

In this paper, we consider central complete and incomplete Bell polynomials which are generalizations of the recently introduced central Bell polynomials and central analogues for the complete and incomplete Bell polynomials. We investigate…

Number Theory · Mathematics 2018-11-06 Taekyun Kim , Dae San Kim , Gwan-Woo Jang

Recently, Kim-Kim introduced the degenerate r-Bell polynomials and investigated some results which are derived from umbral calculus. The aim of this paper is to study some properties of the degenerate r-Bell polynomials and numbers via…

Number Theory · Mathematics 2022-08-11 Taekyun Kim , Dae san Kim , Hye Kyung Kim

In this paper we derive congruences expressing Bell numbers and derangement numbers in terms of each other modulo any prime.

Number Theory · Mathematics 2010-08-10 Zhi-Wei Sun , Don Zagier

The aim of this paper is to study probabilistic versions of the degenerate Whitney numbers of the second kind and those of the degenerate Dowling polynomials, namely the probabilistic degenerate Whitney numbers of the second kind associated…

Number Theory · Mathematics 2023-12-18 Taekyun Kim , Dae San Kim

We introduce the generalized degenerate Euler-Genocchi polynomials as a degenerate version of the Euler-Genocchi polynomials. In addition, we introduce their higher-order version, namely the generalized degenerate Euler-Genocchi polynomials…

Number Theory · Mathematics 2022-08-24 Taekyun Kim , Dae San Kim , Hye Kyung Kim

Spivey's combinatorial method revealed an important identity for Bell numbers, involving Stirling numbers of the second kind. This paper extends his work by deriving Spivey-type recurrence relations for fully degenerate Bell polynomials and…

Number Theory · Mathematics 2025-09-09 Taekyun Kim , Dae San Kim

In combinatorics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. The number of derangement of an n-element set is called the nth derangement number. Recently, the degenerate…

Number Theory · Mathematics 2024-10-15 Taekyun Kim , Dae San Kim

In this paper we consider the weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.

Number Theory · Mathematics 2010-11-25 Taekyun Kim

The aim of this paper is twofold. Firstly, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the…

Number Theory · Mathematics 2023-01-11 Taekyun Kim , Dae San Kim

In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of some identities involving poly-Bernoulli polynomials.

Combinatorics · Mathematics 2022-07-04 Beáta Bényi , Toshiki Matsusaka

In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas…

Number Theory · Mathematics 2019-07-04 Armen Bagdasaryan , Serkan Araci , Mehmet Acikgoz , Yuan He