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We introduce the $B$-Stirling numbers of the first and second kind, which are the coefficients of the potential polynomials when we express them in terms of the monomials and the falling factorials, respectively. These numbers include, as…

Combinatorics · Mathematics 2024-10-17 José A. Adell , Beáta Bényi

In this paper, we study some combinations of the degenerate and incomplete Stirling numbers of the second kind. We use a combinatorial approach and provide some asymptotic results.

Combinatorics · Mathematics 2026-04-21 Beáta Bényi , Sithembele Nkonkobe

This paper introduces a novel generalization of Stirling and Lah numbers, termed ``heterogeneous Stirling numbers," which smoothly interpolate between these classical combinatorial sequences. Specifically, we define heterogeneous Stirling…

General Mathematics · Mathematics 2025-04-01 Taekyun Kim , Dae San Kim

Associated to each complex-valued random variable satisfying appropriate integrability conditions, we introduce a different generalization of the Stirling numbers of the second kind. Various equivalent definitions are provided. Attention,…

Probability · Mathematics 2020-10-20 José A. Adell

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 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

The aim of this paper is twofold. The first one is to find several relations between the type 2 higher-order degenerate Euler polynomials and the type 2 higher-order Changhee polynomials in connection with the degenerate stirling numbers of…

Number Theory · Mathematics 2020-04-28 Taekyun Kim , Dae San Kim

The aim of this paper is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential…

Number Theory · Mathematics 2022-02-11 Taekyun Kim , Dae San Kim

Recently, authors studied the unsigned degenerate r-Stirling number of the first kind and the degenerate r-Stirling number of the second kind, respectively of which are the degenerate versions of the unsigned r-Stirling numbers of the first…

Number Theory · Mathematics 2022-02-18 Taekyun Kim , Dae san Kim

This paper investigates the Stirling numbers of the first and second kind associated with a delta series f (t). These numbers provide a robust framework that satisfies the orthogonality and inverse relations, often lacking in recent…

Number Theory · Mathematics 2026-02-03 Dae san Kim , Taekyun Kim

In this paper, we consider the degenerate Stirling polynomials of the second kind which are derived from the generating function. In addition, we give some new identities for these polynomials.

Number Theory · Mathematics 2017-04-10 Taekyun Kim

This paper has two primary contributions. First, we explore degenerate Sheffer-type polynomials, a hybrid of higher-order degenerate Bernoulli and Euler polynomials, and derive their properties. Second, assuming that the moment generating…

Number Theory · Mathematics 2025-07-29 Taekyun Kim , Dae san Kim

Harmonic numbers have been studied since antiquity, while hyperharmonic numbers were intoduced by Conway and Guy in 1996. The degenerate harmonic numbers and degenerate hyperharmonic numbers are their respective degenerate versions. The aim…

Number Theory · Mathematics 2023-01-10 Hye Kyung Kim , 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

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

In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the…

Number Theory · Mathematics 2018-02-06 Taekyun Kim , Yonghong Yao , Dae San Kim , Hyuck-In Kwon

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

Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to represent arbitrary polynomials in terms of probabilistic Frobenius-Euler polynomials associated with Y and…

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

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

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