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In this paper we study q-Euler numbers and polynomials by using p-adic q-fermionic integrals on Z_p. The methods to study q-Euler numbers and polynomials in this paper are new.

Number Theory · Mathematics 2009-11-13 Taekyun Kim , Min-Soo Kim , Leechae Jang , Seog-Hoon Rim

In this paper, we consider degenerate Carlitz's type q-Euler polynmials and numbers and we investigate some identities arising from the fermionic p-adic integral equations and the generating function of thoe polynomials.

Number Theory · Mathematics 2015-07-17 Dmitry V. Dolgy , Taekyun Kim , Jin-Woo Park , Jong-Jin Seo

Recently, Araci-Acikgoz-Sen derived some interesting identities on weighted q-Euler polynomials and higher-order q-Euler polynomials from the applications of umbral calculus (See [1]). In this paper, we develop the new method of q-umbral…

Number Theory · Mathematics 2013-07-01 Dae San Kim , Taekyun Kim

In this paper we study that the $q$-Euler numbers and polynomials are analytically continued to $E_q(s)$. A new formula for the Euler's $q$-Zeta function $\zeta_{E,q}(s)$ in terms of nested series of $\zeta_{E,q}(n)$ is derived. Finally we…

Number Theory · Mathematics 2008-01-04 T. Kim

The purpose of this paper is to construct q-Euler numbers and polynomials by using p-adic q-integral equations on Zp. Finally, we will give some interesting formulae related to these q-Euler numbers and polynomials.

Number Theory · Mathematics 2009-11-11 Taekyun Kim

In this paper, we investigate some interesting properties of q-Berstein polynomials realted to q-Euler numbers by using the fermionic q-integral on Zp.

Number Theory · Mathematics 2010-10-20 Taekyun Kim

The present paper deals with Bernstein polynomials and Frobenius-Euler numbers and polynomials. We apply the method of generating function and fermionic p-adic integral representation on Zp, which are exploited to derive further classes of…

Number Theory · Mathematics 2012-06-21 Serkan Araci , Mehmet Acikgoz

In this research announcement we present a new q-analog of a classical formula for the exponential generating function of the Eulerian polynomials. The Eulerian polynomials enumerate permutations according to their number of descents or…

Combinatorics · Mathematics 2007-05-23 John Shareshian , Michelle L. Wachs

The aim of this paper is to construct new Dedekind type sums. We construct generating functions of Barnes' type multiple Frobenius-Euler numbers and polynomials. By applying Mellin transformation to these functions, we define Barnes' type…

Number Theory · Mathematics 2018-11-19 Mehmet Cenkci , Yilmaz Simsek , Mumun Can , Veli Kurt

In the present paper, we introduce Eulerian polynomials attached to by using p-adic q-integral on Zp . Also, we give new interesting identities via the generating functions of Dirichlet's type of Eulerian polynomials. After, by applying…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Deyao Gao

In this paper, we consider the new q-extension of Frobenius-Euler numbers and polynomials and we derive some interesting identities from the orthogonality type properties for the new q-extension of Frobenius-Euler polynomials. Finally we…

Number Theory · Mathematics 2013-07-08 Taekyun Kim

By using $q$-Volkenborn integration and uniform differentiable on $\mathbb{Z}%_{p}$, we construct $p$-adic $q$-zeta functions. These functions interpolate the $q$-Bernoulli numbers and polynomials. The value of $p$-adic $q$-zeta functions…

Number Theory · Mathematics 2007-05-23 T. Kim , Y. Simsek , H. M. Srivastav

In this work, we consider the generating function of Kim's q-Euler polynomials and introduce new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give surprising identities for studying in Analytic Numbers…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Jong Jin Seo

The fundamental objective of this paper is to obtain some interesting properties for $\left(h,q\right)$-Genocchi numbers and polynomials by using the fermionic $p$-adic $q$-integral on $\mathbb{Z}_{p}$ and mentioned in the paper…

Number Theory · Mathematics 2014-09-16 Armen Bagdasaryan , Erdogan Sen , Yuan He , Serkan Araci , Mehmet Acikgoz

In this paper, we will constructed p-adic twisted q-l-functions which is a part of answer of the question in [8]. Finally, we will treat many interesting properties related to twisted q-Euler numbers and polynomials.

Number Theory · Mathematics 2007-05-23 S. H. Rim , Y. Simsek , V. Kurt , T. Kim

The purpose of this paper is to present a systemic study of some families of q-Euler numbers and polynomials of Norlund's type by using multivariate fermionic p-adic integral on Zp. Moreover, the study of these higher-order q-Euler numbers…

Number Theory · Mathematics 2009-01-15 Taekyun Kim

By using q-Volkenborn integral on Z_{p}, we (simsek, simsekCanada) constructed new generating functions of the (h,q)-Bernoulli polynomials and numbers. By applying the Mellin transformation to the generating functions, we constructed…

Number Theory · Mathematics 2018-11-19 Yilmaz Simsek

The main purpose of this paper is to provide a novel approach to deriving formulas for the p-adic q-integral including the Volkenborn integral and the p-adic fermionic integral. By applying integral equations and these integral formulas to…

Number Theory · Mathematics 2024-04-18 Yilmaz Simsek

Recently, the higher-order q-Euler polynomials and multiple q-Euler zeta functions are introduced by T. Kim ([8, 9]). In this paper, we investigate some symmetric properties of the multiple q-Euler zeta function and derive various…

Number Theory · Mathematics 2013-12-30 Dae San Kim , Taekyun Kim

In the present paper, our goal is to introduce a p-adic continuous function for an odd prime to inside a p-adic q-analogue of the higher order dedekind-type sums with weight alpha related to Extended q-Euler polynomials by using p-adic…

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