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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 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 derive some new and interesting idebtities for Bernoulli, Euler and Hermite polynomials associated with Chebyshev polynomials.

Number Theory · Mathematics 2012-11-08 Dae San Kim , Taekyun Kim , Sang-Hun Lee

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

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

In this paper, we give some interesting identities of higher-order Bernoulli, Frobenius-Euler and Euler polynomials arising from umbral calculus. From our method of this paper, we can derive many interesting identities of special…

Number Theory · Mathematics 2013-02-27 Taekyun Kim , Dae San Kim

In this paper, we consider Hermite and poly-Bernoulli mixed-type polynomials and investigate the properties of those polynomials which are derived from umbral calculus. Finally, we give various identities associated with Stirling numbers,…

Number Theory · Mathematics 2013-10-07 Dae san Kim , taekyun Kim

In this paper we give some relation involving values of q-Bernoulli, q-Euler and Bernstein polynomials. From these relations, we obtain some interesting identities on the q-Bernoulli, q-Euler and Bernstein polynomials.

Number Theory · Mathematics 2015-05-27 A. Bayad , T. Kim

In this paper, we consider higher-order Bernoulli and poly-Bernoulli mixed type polynomials and we give some interesting identities of those polynomials arising from umbral calculus.

Number Theory · Mathematics 2013-07-09 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

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

We derive several symmetric identities for Bernoulli and Euler polynomials which imply some known identities. Our proofs depend on the new technique developed in part I and some identities obtained in [European J. Combin. 24(2003),…

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

In this paper, we consider higher-order Frobenius-Euler polynomi- als associated with poly-Bernoulli polynomials which are derived from polylogarithmic function. These polynomials are called higher-order Frobenius-Euler and poly-Bernoulli…

Number Theory · Mathematics 2013-07-12 Dae San Kim , Taekyun kim

In this paper we investigate some properties for the q-Euler numbers ans polymials. From these properties we give some identities on the Bernstein polymials and q-Euler polynpmials.

Number Theory · Mathematics 2011-01-14 Abdelmejid Bayad , Taekyun Kim , Byunje Lee , Seog-Hoon Rim

In this paper, we consider Barnes' multiple Bernoulli and poly-Bernoulli mixed-type polynomials. From the properties of Sheffer sequences of these polynomials arising from umbrral calculus, we derive new and interesting identities.

Number Theory · Mathematics 2013-12-30 D. S. Kim , T. Kim , T. Komatsu

In this paper, we give new identities involving Phillips q-Bernstein polynomials and we derive some interesting properties of q-Berstein polynomials associated with q-Stirling numbers and q-Bernoulli polynomials.

Number Theory · Mathematics 2010-08-27 T. 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

In this paper we give new identities involving q-Euler polynomials of higher order.

Number Theory · Mathematics 2015-05-14 Taekyun Kim , Y. H. Kim

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

The relations between the Bernoulli and Eulerian polynomials of higher order and the complete Bell polynomials are found that lead to new identities for the Bernoulli and Eulerian polynomials and numbers of higher order. General form of…

Number Theory · Mathematics 2009-11-17 Boris Y. Rubinstein
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