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The degenerate Stirling numbers of the second kind and of the first kind, which are respectively degenerate versions of the Stirling numbers of the second kind and of the first kind, appear frequently when we study various degenerate…

Number Theory · Mathematics 2022-06-10 Taekyun Kim , Dae san Kim , Hye Kyung 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 derangement polynomials, the derangement polynomials of type 2…

Probability · Mathematics 2024-01-09 Taekyun Kim , Dae San 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

Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…

Number Theory · Mathematics 2020-02-12 Taekyun Kim , Dae San Kim

In this paper, we study degenerate ordered Bell polynomials with the viewpoint of Carlitz's degenerate Bernoulli and Euler polynomials and derive by using umbral calculus some properties and new identities for the degenerate ordered Bell…

Number Theory · Mathematics 2017-04-25 Taekyun Kim , Dae san Kim

The study of degenerate versions of certain special polynomials and numbers, which was initiated by Carlitz's work on degenerate Euler and degenerate Bernoulli polynomials, has recently seen renewed interest among mathematicians. The aim of…

Number Theory · Mathematics 2025-01-13 Taekyun Kim , Dae san Kim

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

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

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

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

In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number. In this paper, as natural companions to derangement numbers and degenerate…

Number Theory · Mathematics 2017-12-12 Taekyun Kim , Dae san Kim

Assume that Y is a random variable whose moment generating function exists in a neighborhood of the origin. We study the probabilistic degenerate r-Stirling numbers of the second kind associated with Y and the probabilistic degenerate…

Number Theory · Mathematics 2024-05-24 Taekyunj Kim , Dae San Kim

I recent years, many mathematicians studied various degenerate version of some spcial polynomials of which quite a few interesting results were discovered. In this paper, we introduce the type 2 degenerate Bernoulli polynomials of the…

Number Theory · Mathematics 2019-08-20 Taekyun Kim , Lee-Chae jang , Dae San Kim , Han-Young 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

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

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

Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…

Combinatorics · Mathematics 2022-10-19 Yuankui Ma , Taekyun Kim , Hongze Li

In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated…

Number Theory · Mathematics 2024-10-08 Jinyu Wang , Yuankui Ma , Taekyun Kim , Dae San 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

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