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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 introduce the degenerate gamma random variables which are connected with the degenerate gamma functions and the degenerate exponential functions, and deduce the expectation and variance of those random variables.

Probability · Mathematics 2020-04-21 Taekyun Kim , Dae san Kim , Jongkyum Kwon , Hyunseok Lee

In recent years, some degenerate versions of quite a few special numbers and polynomials are introduced and investigated by means of various methods. The aim of this paper is to study some results on degenerate harmonic numbers, degenerate…

Number Theory · Mathematics 2022-08-30 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

Recently, several authors have studied the degenerate Bernoulli and Euler polynomials and given some intersting identities of those polynomials. In this paper, we consider the degenerate Bell numbers and polynomials and derive some new…

Number Theory · Mathematics 2015-07-09 Taekyun Kim , Dae san Kim

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

Carlitz [2] initiated a study on degenerate versions of Bernoulli and Euler numbers which has been extended recently to the researches on various degenerate versions of quite a few special numbers and polynomials. They have been explored by…

Number Theory · Mathematics 2021-06-28 Taekyun Kim , Dae san Kim , Hyunseok Lee , Seong Ho Park , Jongkyum Kwon

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

We introduce the degenerate Bernoulli numbers of the second kind as a degenerate version of the Bernoulli numbers of the second kind. We derive a family of nonlinear differential equations satisfied by a function closely related to the…

Number Theory · Mathematics 2018-04-27 Taekyun Kim , Dae San Kim

In 2008, Spivey found a recurrence relation for the Bell numbers. We consider the probabilistic r-Bell polynomials associated with which are a probabilistic extension of the r-Bell polynomials. Here Y is a random variable whose moment…

Number Theory · Mathematics 2024-04-04 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, 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

In this paper, we consider the degenerate multi-poly-Bernoulli numbers and polynomials which are defined by means of the multiple polylogarithms and degenerate versions of the multi-poly-Bernoulli numbers and polynomials. We investigate…

Number Theory · Mathematics 2020-05-18 Taekyun Kim , Dae San Kim

In this paper, we consider the degenerate Changhee numbers and polynomials of the second kind which are different from the previously introduced degenerate Changhee numbers and polynomials by Kwon-Kim-Seo (see [11]). We investigate some…

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

The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate Stirling numbers of both kinds associated with degenerate hyperharmonic numbers and also with degenerate Bernolli, degenerate…

Number Theory · Mathematics 2023-04-05 Taekyun Kim , Dae San Kim

It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results. The aim of this paper is to study the generalized degenerate…

Number Theory · Mathematics 2023-05-09 Taekyun Kim , Dae San Kim , Hye Kyung Kim

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 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 satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures…

Number Theory · Mathematics 2026-01-16 Taekyun Kim , Dae San Kim

Recently, several authors have studied the Stirling numbers of the second kind and Bell polynomials. In this paper, we study the extended Stirling polynomials of the second kind and the extended Bell polynomials associated with the Stirling…

Number Theory · Mathematics 2017-05-24 Taekyun Kim , Dae san Kim