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In this paper, we present a new definition and generalization of higher order Daehee of the first and second kind. Some new results for these polynomials and numbers are derived. Furthermore, some interesting special cases of the new…

General Mathematics · Mathematics 2021-03-26 F. M. Abdel Moneim , A. Mustafa , B. S. El-Desouky

We derive new matrix representation for higher-order changhee numbers and polynomials. This helps us to obtain simple and short proofs of many previous results on higher-order changhee numbers and polynomials. Moreover, we obtain recurrence…

Combinatorics · Mathematics 2019-09-16 Beih S. El-Desouky , Abdelfattah Mustafa , Nenad P. Cakic

Recently, Daehee numbers and polynomials are introduced by the authors. In this paper, we consider the Daehee numbers and polynomials of order k and give some relation between Daehee polynomials of order k and special polynomials

Number Theory · Mathematics 2013-10-18 Dae San Kim , Taekyun Kim

We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…

Combinatorics · Mathematics 2015-03-03 B. S. El-Desouky , Abdelfattah Mustafa

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

Recently, Komatsu introduced the concept of poly-Cauchy numbers and polynomials which generalize Cauchy numbers and polynomials. In this paper, we consider the new concept of higher-order Cauchy numbers and polynomials which generalize…

Number Theory · Mathematics 2013-10-15 Dae san Kim , Taekyun Kim

In this paper, we consider the higher-order Changhee numbers and polynomials which are derived from the fermionic p-adic integral on Zp and give some relations between higher-order Changhee polynomials and special polynomials.

Number Theory · Mathematics 2013-10-29 Dae San Kim , Taekyun Kim

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

In this paper, we study a degenerate version of the Daehee polynomials and numbers, namely the degenerate Daehee polynomials and numbers, which were recently introduced by Jang et. al. We derive their explicit expressions and some…

Number Theory · Mathematics 2020-04-21 Taekyun Kim , Dae San Kim , Han Young Kim , Jongkyum Kwon

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 this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations…

Number Theory · Mathematics 2010-02-03 Ayhan Dil , Veli Kurt

The new method for obtaining a variety of extensions of Hermite polynomials is given. As a first example a family of orthogonal polynomial systems which includes the generalized Hermite polynomials is considered. Apparently, either these…

Quantum Algebra · Mathematics 2007-05-23 Vadim V. Borzov

Recently, the non-linear Changhee differential equations were introduced in [5] and these differential equations turned out to be very useful for studying special polynomials and mathematical physics. Some interesting identities and…

Number Theory · Mathematics 2016-03-01 Dmitry V. Dolgy , Dae san Kim , Taekyun Kim , Jong-Jin Seo

In this paper, we investigate some properties of the associated sequence of Daehee and Changhee polynomials. Finally, we give some interesting identities of associated sequence involving some special polynomials.

Number Theory · Mathematics 2013-01-29 D. S. Kim , T. Kim , S. -H. Rim

Thw purpose of this paper is to present a systemic study of some families of the generalized q-Euler numbers and polynomials of higher order.

Number Theory · Mathematics 2009-12-25 Taekyun Kim

In this paper, we derive new matrix representation for Daehee numbers and polynomials, the lambda-Daehee numbers and polynomials and the twisted Daehee numbers and polynomials. This helps us to obtain simple and short proofs of many…

Combinatorics · Mathematics 2014-12-30 B. S. El-Desouky , Abdelfattah Mustafa

In this note we give a generalization for the higher order Hochschild cohomology and show that the secondary Hochschild cohomology is a particular case of this new construction.

Rings and Algebras · Mathematics 2016-07-26 Bruce R. Corrigan-Salter , Mihai D. Staic

In this paper, we consider the Carlitz's type q-analogue of Changhee numbers and polynomials and we give some explicit formulae for these numbers and polynomials.

Number Theory · Mathematics 2017-08-23 D. V. Dolgy , G. W. Janf , H. I. Kwon , T. Kim

We consider the Witt-type formula for Daehee numbrers and polynomials and investigate some properties of those numbers and polynomials. In particular, Daehee numbers are closely related to higher-order Bernoulli numbers and Bernoulli…

Number Theory · Mathematics 2013-09-10 Dae San Kim , Taekyun 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
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