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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

In this paper, we study the degenerate derangement polynomials and numbers, investigate some properties of those polynomials and numbers and explore their connections with the degenerate gamma distributions. In more detail, we derive their…

Number Theory · Mathematics 2020-11-18 Taekyun Kim , Dae san Kim , Hyunseok Lee , Lee-Chae Jang

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

This paper introduces and investigates degenerate versions of the A-algorithm and B-algorithm by incorporating a parameter lambda into their respective recurrence relations. We derive explicit formulas for the final sequences of these…

Number Theory · Mathematics 2026-01-05 Taekyun Kim , Dae san Kim

In this paper, we introduce degenertae generalized hypergeometric functions and study degenerate hypergeometric numbers of order p. These numbers involving of lambda-binomial coefficients and lambda-falling sequence, and can be represented…

Number Theory · Mathematics 2019-09-02 Taekyun Kim , Dae San Kim , Hyunseok 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

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 define multi poly-Bernoulli polynomials using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. Furthermore, an explicit formula for certain Hurwitz-Lerch type multi…

Combinatorics · Mathematics 2016-07-14 Roberto B. Corcino , Hassan Jolany , Cristina B. Corcino , Takao Komatsu

In this paper, we consider higher-order Bernoulli and poly-Bernoulli mixed type polynomials and we give some interesting identities of those polynomials arising from umbral calculus.

Number Theory · Mathematics 2013-07-09 Dae San Kim , Taekyun 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

Let Y be a random variable such that the moment generating function of Y exists in a neighborhood of the origin. The aim of this paper is to study probabilistic versions of the degenerate Fubini polynomials and the degenerate Fubini…

Probability · Mathematics 2024-01-08 Rongrong Xu , Taekyun Kim , Dae San Kim , Yuankui Ma

The operational calculus associated with special polynomials has proven to be a powerful tool for analyzing and simplifying their properties. This article examines the bivariate degenerate Hermite polynomials with a focus on their…

Classical Analysis and ODEs · Mathematics 2025-09-01 Nusrat Raza , Ujair Ahmad , Subuhi Khan

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

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

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

In this paper, we consider Hermite and poly-Bernoulli mixed-type polynomials and investigate the properties of those polynomials which are derived from umbral calculus. Finally, we give various identities associated with Stirling numbers,…

Number Theory · Mathematics 2013-10-07 Dae san 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

Many works have been done in recent years as to explorations for degenerate versions of some special polynomials and numbers, which began with the introduction of the degenerate Bernoulli and degenerate Euler polynomials by Carlitz. The aim…

Number Theory · Mathematics 2022-12-13 Taekyun Kim , Dae San Kim , Jongkyum Kwon

The aim of this paper is to introduce the degenerate generalized Laguerre polynomials as the degenerate version of the generalized Laguerre polynomials and to derive some properties related to those polynomials and Lah numbers, including an…

Classical Analysis and ODEs · Mathematics 2021-07-07 Taekyun Kim , Dmitry V. Dolgy , Dae san Kim , Hye Kyung Kim , Seong Ho Park

Recently, several types of degenerate Bell polynomials have been introduced as degenerate versions of the ordinary Bell polynomials. The aim of this paper is to study some identities for the degenerate Bell polynomials and their related…

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