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In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.

Number Theory · Mathematics 2015-07-20 Taekyun Kim , Hyuck-In Kwon , Jong-Jin Seo

In this paper, we study degenerate ordered Bell polynomials with the viewpoint of Carlitz's degenerate Bernoulli and Euler polynomials and derive by using umbral calculus some properties and new identities for the degenerate ordered Bell…

Number Theory · Mathematics 2017-04-25 Taekyun Kim , Dae san Kim

A construction of new sequences of generalized Bernoulli polynomials of first and second kind is proposed. These sequences share with the classical Bernoulli polynomials many algebraic and number--theoretical properties. A new class of…

Number Theory · Mathematics 2021-12-16 Piergiulio Tempesta

In this paper we derive some interesting identities arising from the orhtogonality of gegenbauer polynomials.

Number Theory · Mathematics 2012-08-01 Dae San Kim , Taekyun Kim , Seog-Hoon Rim

In this paper, we study the degenerate Eulerian polynomials and numbers and give some new and interesting identities associated with several special numbers and polynomials.

Number Theory · Mathematics 2017-05-04 Taekyun Kim , Dae san kim

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

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 study the degenerate version of the new type Euler polynomials, namely degenerate cosine-Euler polynomials and sime-Euler polynomials and also corresponding ones for Bernoulli polynomials, namely degenerate cosine…

Number Theory · Mathematics 2019-08-13 Dae San Kim , Taekyun kim , Hyunseok Lee

We investigate some interesting properties of Bernstein polynomials associated with boson p-adic integrals on Zp.

Number Theory · Mathematics 2010-09-02 M. S. Kim , T. Kim , B. Lee , C. S. Ryoo

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

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 define multi poly-Bernoulli polynomials using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. Furthermore, an explicit formula for certain Hurwitz-Lerch type multi…

Combinatorics · Mathematics 2016-07-14 Roberto B. Corcino , Hassan Jolany , Cristina B. Corcino , Takao Komatsu

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 study relations among several types of Eulerian polynomials from a combinatorial viewpoint. We establish an identity between the restricted Eulerian polynomials of types $A$ and $B$. As an application, we present a…

Combinatorics · Mathematics 2026-03-04 Zhong-Xue Zhang

Recently, several authors have studied the degenerate Bernoulli and Euler polynomials and given some intersting identities of those polynomials. In this paper, we consider the degenerate Bell numbers and polynomials and derive some new…

Number Theory · Mathematics 2015-07-09 Taekyun Kim , Dae san Kim

In recent years, studying degenerate versions of various special polynomials and numbers have attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials and…

Number Theory · Mathematics 2019-03-12 Dae San Kim , Han Young Kim , Sung-Soo Pyo , Taekyun Kim

In this paper, we consider Poisson-Charlier and poly-Cauchy mixed type polynomials and give various identities of those polynomials which are derived from umbral calculus.

Number Theory · Mathematics 2013-09-05 Dae San Kim , Taekyun 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

By the symmetric properties of Drichlet's type multiple q-l-function, we establish various identities concerning the generalized higher-order q-Euler polynomials. Furthermore, we give some interesting relationship between the power sums and…

Number Theory · Mathematics 2013-12-31 Dae San Kim , Taekyun Kim

In this paper, we derive novel formulas and identities connecting Cauchy numbers and polynomials with both ordinary and generalized Stirling numbers, binomial coefficients, central factorial numbers, Euler polynomials, $r$-Whitney numbers,…

Combinatorics · Mathematics 2025-10-07 José L. Cereceda