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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

In this paper, we consider degenerate poly-Bernoulli numbers and polynomials associated with polylogarithmic function and p-adic invariant integral on Zp. By using umbral calculus, we derive some identities of those numbers and polynomials

Number Theory · Mathematics 2015-06-11 Dae San Kim , Taekyun Kim

In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials…

Number Theory · Mathematics 2017-06-30 Taekyun Kim , Dae San Kim

In recent years, studying degenerate versions of various special polynomials and numbers have attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials and…

Number Theory · Mathematics 2019-03-12 Dae San Kim , Han Young Kim , Sung-Soo Pyo , Taekyun Kim

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, 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

We discuss a special function (polyexponential) that extends the natural exponential function and also the exponential integral. The basic properties of the polyexponential are listed and some applications are given. In particular, it is…

Numerical Analysis · Mathematics 2007-10-09 Khristo N. Boyadzhiev

In this paper, we study the degenerate Eulerian polynomials and numbers and give some new and interesting identities associated with several special numbers and polynomials.

Number Theory · Mathematics 2017-05-04 Taekyun Kim , Dae san kim

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

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

In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.

Number Theory · Mathematics 2015-07-20 Taekyun Kim , Hyuck-In Kwon , Jong-Jin Seo

Recently, the degenerate Stirling numbers of the first kind were introduced. In this paper, we give some formulas for the degenerate Stirling numbers of the first kind in the terms of the complete Bell polynomials with higher-order harmonic…

Number Theory · Mathematics 2018-02-06 Taekyun Kim , Dae San 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, T. Kim considered Euler zeta function which interpolates Euler polynomials at negative integer (see [3]). In this paper, we study degenerate Euler zeta function which is holomorphic function on complex s-plane associated with…

Number Theory · Mathematics 2016-01-20 Taekyun Kim

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

In this paper, we consider the degenerate Daehee numbers and polynomials of the second kind which are different from the previously introduced Daehee numbers and polynomials. We investigate some properties of these numbers and polynomials.…

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

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

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

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

In this paper, we consider degenerate Carlitz's type q-Euler polynmials and numbers and we investigate some identities arising from the fermionic p-adic integral equations and the generating function of thoe polynomials.

Number Theory · Mathematics 2015-07-17 Dmitry V. Dolgy , Taekyun Kim , Jin-Woo Park , Jong-Jin Seo