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Related papers: Degenerate Bernstein Polynomials

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In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.

Number Theory · Mathematics 2015-03-31 Dae San Kim , Taekyun 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

The aim of this paper is to study degenerate Eulerian polynomials and degenerate Eulerian numbers, respectively as degenerate versions of the Eulerian polynomials and the Eulerian numbers, and to derive some of their properties.…

Number Theory · Mathematics 2024-12-05 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

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

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

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

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 twofold. Firstly, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the…

Number Theory · Mathematics 2023-01-11 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 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

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

In this paper, we study the Carlitz's degenerate Bernoulli numbers and polynomials and give some formulae and identities related to those numbers and polynomials.

Number Theory · Mathematics 2015-06-16 Taekyun Kim , Dae San Kim , Hyuck-In Kwon

As is well-known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate version of such functions and polynomials, degenerate polylogarithm functions were introduced and degenertae…

Number Theory · Mathematics 2020-12-14 Taekyun Kim , Dae San Kim , Jongkyum Kwon , Hyunseok Lee

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

We introduce new generalizations of the Bernoulli, Euler, and Genocchi polynomials and numbers based on the Carlitz-Tsallis degenerate exponential function and concepts of the Umbral Calculus associated with it. Also, we present…

Number Theory · Mathematics 2018-11-07 Orli Herscovici , Toufik Mansour

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

In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.

Number Theory · Mathematics 2015-07-20 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

Main purpose of this paper is to reconstruct generating function of the Bernstein type polynomials. Some properties this generating functions are given. By applying this generating function, not only derivative of these polynomials but also…

Classical Analysis and ODEs · Mathematics 2011-12-12 Yilmaz Simsek
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