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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 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

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 various speical mixed-type polynomials which are related to Bernoulli, Euler, Changhee and Daehee polynomials. From those polynomials, we derive some interesting and new identities

Number Theory · Mathematics 2014-06-10 Dae San Kim , Taekyun Kim , Hyucj In Kwon

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

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 paper, we consider Barnes-type Daehee polynomials of the first kind and of the second kind. From the properties of Sheffer sequences of these polynomials arising from umbral calculus, we derive new and interesting identities.

Number Theory · Mathematics 2014-01-15 Dae San Kim , Taekyun Kim , Takao Komatsu , Jong-Jin Seo

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 weighted q-Bernoulli numbers and polynomials which are differnt type of Carlitz's q-Bernoulli numbers and polynomials. From these numbers and polynomials, we derive some interesting formulaes and identities.

Number Theory · Mathematics 2010-11-25 Taekyun Kim

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

In this paper, we consider the poly-Bernoulli numbers and polynomials of the second kind and presents new and explicit formulae for calculating the poly-Bernoulli numbers of the second kind and the Stirling numbers of the second kind.

Number Theory · Mathematics 2014-06-25 Taekyun Kim , Sang-Hun Lee , Jongjin Seo

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 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

Boole polynomials play an important role in the area of number theory, algebra and umbral calculus. In this paper, we investigate some properties of Boole polynomials and consider Witt-type formulas for the Boole numbers and polynomials.…

Number Theory · Mathematics 2013-10-31 Dae San Kim , Taekyun Kim

In this paper we consider the Daehee numbers and polynomials of the first and second kind, and give several explicit representations for them. In particular, we express the Daehee polynomials as the derivative of a generalized binomial…

Number Theory · Mathematics 2021-08-20 José L. Cereceda

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

The Stirling numbers of the first kind can be represented in terms of a new class of polynomials that are closely related to the Bernoulli polynomials. Recursion relations for these polynomials are given.

Mathematical Physics · Physics 2007-05-23 Carl M. Bender , Dorje C. Brody , Bernhard K. Meister

In this paper we study q-Bernoulli numbers and polynomials related to q-Stirling numbers. From thsese studying we investigate some interesting q-stirling numbers' identities related to q-Bernoulli numbers.

Number Theory · Mathematics 2007-10-29 Taekyun Kim

In this paper, we introduce new generalizations of higher-order Changhee of the first and second kind. Moreover, we derive some new results for these numbers and polynomials. Furthermore, some interesting special cases of the generalized…

General Mathematics · Mathematics 2021-03-19 F. M. Abdel Moneim , Abdelfattah Mustafa , B. S. El-Desouky
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