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The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.

Number Theory · Mathematics 2009-12-31 Taekyun Kim

In this paper, we will deal with some new formulae for two product Genocchi polynomials together with both Euler polynomials and Bernoulli polynomials. We get some applications for Genocchi polynomials. Our applications possess a number of…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Erdoğan Şen

As is well-known, poly-Bernoulli polynomials are defined in terms of polylogarithm functions. Recently, as degenerate version of such functions and polynomials, degenerate polylogarithm functions were introduced and degenertae…

Number Theory · Mathematics 2020-12-14 Taekyun Kim , Dae San Kim , Jongkyum Kwon , Hyunseok Lee

In this paper, we investigate some identities of Laguerre polynomials involving Bernoulli and Euler polynomials which are derived from umbral calculus.

Number Theory · Mathematics 2015-06-12 Taekyun Kim

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

In this paper, we provide some novel binomial convolution related to symmetric functions, as well as convolution sums without the binomial symbol. Moreover we give some new convolution sums of Bernoulli, Euler, and Genocchi numbers and…

Combinatorics · Mathematics 2025-04-30 Meryem Bouzeraib , Ali Boussayoud , Salah Boulaaras

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

The study of degenerate versions of certain special polynomials and numbers, which was initiated by Carlitz's work on degenerate Euler and degenerate Bernoulli polynomials, has recently seen renewed interest among mathematicians. The aim of…

Number Theory · Mathematics 2025-01-13 Taekyun Kim , Dae san Kim

In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials and more generally of the higher-order degenerate Bernoulli polynomials. We derive explicit formulas with the help of…

Number Theory · Mathematics 2021-08-12 Dae san Kim , Taekyun Kim

In this paper, we consider the degenerate poly-Bernoulli polynomials and present new and explicit formulas for computing them in terms of the degenerate Bernoulli polynomials and Stirling numbers of the second kind.

Number Theory · Mathematics 2015-03-31 Dae San Kim , Taekyun Kim

Studying degenerate versions of various special polynomials have become an active area of research and yielded many interesting arithmetic and combinatorial results. Here we introduce a degenerate version of polylogarithm function, called…

Number Theory · Mathematics 2020-02-12 Taekyun Kim , Dae San Kim

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 [Arch. Math. 7, 28 (1956), Utilitas Math. 15, 51 (1979)] Carlitz introduced the degenerate Bernoulli numbers and polynomials by replacing the exponential factors in the corresponding classical generating functions with their deformed…

Mathematical Physics · Physics 2016-12-23 M. Balamurugan , R. Chakrabarti , R. Jagannathan

In this paper, we introduce the new fully degenerate poly-Bernoulli numbers and polynomials and investigate some properties of these polynomials and numbers. From our properties, we derive some identities for the fully degenerate…

Number Theory · Mathematics 2015-05-27 Dae San Kim , Taekyun 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

The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate Stirling numbers of both kinds associated with degenerate hyperharmonic numbers and also with degenerate Bernolli, degenerate…

Number Theory · Mathematics 2023-04-05 Taekyun Kim , Dae San Kim

We give a new construction of q-Genocchi numbers, Euler numbers of higher order, which are different than the q-Genocchi numbers of Cangul-Ozden-Simsek. By using our q-Genoucchi, Euler nimbers of higher order, we can investigate the…

Number Theory · Mathematics 2009-01-06 Taekyun Kim

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

Recently, Masjed-Jamei-Beyki-Koepf studied the so called new type Euler polynomials without making use of Euler polynomials of complex variable. Here we study degenerate and type 2 versions of these new type Euler polynomials, namely the…

Number Theory · Mathematics 2019-08-30 Taekyun Kim , Dae san Kim , Lee-Chae Jang , Han-Young Kim

This paper has two primary contributions. First, we explore degenerate Sheffer-type polynomials, a hybrid of higher-order degenerate Bernoulli and Euler polynomials, and derive their properties. Second, assuming that the moment generating…

Number Theory · Mathematics 2025-07-29 Taekyun Kim , Dae san Kim