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Related papers: A note on degenerate Euler and Bernoulli polynomia…

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In this article, we introduce combinatorial models for poly-Bernoulli polynomials and poly-Euler numbers of both kinds. As their applications, we provide combinatorial proofs of some identities involving poly-Bernoulli polynomials.

Combinatorics · Mathematics 2022-07-04 Beáta Bényi , Toshiki Matsusaka

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 a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials…

Number Theory · Mathematics 2017-06-30 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 this paper, we study umbral calculus to have alternative ways of obtaining our results. That is, we derive some interesting identities of the higher-order Bernoulli, Euler and Hermite polynomials arising from umbral calculus to have…

Number Theory · Mathematics 2013-02-22 Taekyun Kim , Dae San Kim , Seog-Hoon Rim , Dmitry v. Dolgy

We prove certain identities involving Euler and Bernoulli polynomials that can be treated as recurrences. We use these and also other known identities to indicate connection of Euler and Bernoulli numbers with entries of inverses of certain…

Rings and Algebras · Mathematics 2014-03-06 Paweł J. Szabłowski

According to generalized Mellin derivative (Kargin), we introduce a new family of polynomials called higher order generalized geometric polynomials. We obtain some properties of them.We discuss their connections to degenerate Bernoulli and…

Classical Analysis and ODEs · Mathematics 2019-08-01 Levent Kargin , Bayram Çekim

We investigate the representation of arbitrary polynomials using probabilistic Bernoulli and degenerate Bernoulli polynomials associated with a random variable $Y$, whose moment generating function exists in a neighborhood of the origin. In…

Number Theory · Mathematics 2025-10-27 Dae san Kim , Taekyun Kim

In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…

Number Theory · Mathematics 2014-01-28 Hassan Jolany , Mohsen Aliabadi , Roberto B. Corcino , M. R. Darafsheh

In the present paper, we obtain new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived using a Bernoulli polynomial basis. Finally, by utilizing our method, we also derive formulas…

Number Theory · Mathematics 2019-07-04 Armen Bagdasaryan , Serkan Araci , Mehmet Acikgoz , Yuan He

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

The aim of this paper is to further study some properties and identities on the degenerate Fubini and the degenerate Bell polynomials which are degenerate versions of the Fubini and the Bell polynomials, respectively. Especially, we find…

Number Theory · Mathematics 2022-03-02 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

In recent years, many authors have studied Changhee and Dae- hee polynomials in connection with many special numbers and polynomials. In this paper, we investigate type 2 Changhee and Daehee numbers and polynomials and give some identities…

Number Theory · Mathematics 2018-09-17 Dae San Kim , Taekyun 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 obtain several new identities for Bernoulli and Euler polynomials; some of them extend Miki's and Matiyasevich's identities. Our new method involves differences and derivatives of polynomials.

Number Theory · Mathematics 2007-05-23 Hao Pan , Zhi-Wei Sun

Recently, Kim-Kim introduced the lambda-umbral calculus, in which the lambda-Sheffer sequences occupy the central position. In this paper, we introduce the fully degenerate Bell and the fully degenerate Dowling polynomials, and investigate…

Number Theory · Mathematics 2023-01-11 Yuankui Ma , Taekyun Kim , Hyunseok Lee , Dae San 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 present grammatical descriptions of several polynomials associated with Eulerian polynomials, including q-Eulerian polynomials, alternating run polynomials and derangement polynomials. As applications, we get several…

Combinatorics · Mathematics 2016-09-20 Shi-Mei Ma , Jun Ma , Yeong-Nan Yeh , Bao-Xuan Zhu

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