English
Related papers

Related papers: A Unified Generating Function of the q-Genocchi Po…

200 papers

The q-calculus theory is a novel theory that is based on finite difference re-scaling. The rapid development of q-calculus has led to the discovery of new generalizations of q-Euler polynomials involving q-integers. The present paper deals…

Number Theory · Mathematics 2013-08-02 Serkan Araci , Mehmet Acikgoz , Hassan Jolany

In this paper we give the q-extension of Euler numbers which can be viewed as interpolating of the q-analogue of Euler zeta function ay negative integers, in the same way that Riemann zeta function interpolates Bernoulli numbers at negative…

Number Theory · Mathematics 2008-07-18 Taekyun Kim

Using non-archimedean q-integrals on Zp defined in [15, 16], we define a new Changhee q-Euler polynomials and numbers which are different from those of Kim [7] and Carlitz [2]. We define generating functions of multiple q-Euler numbers and…

Number Theory · Mathematics 2007-05-23 Taekyun Kim , SAeog-Hoon Rim

The main object of this paper is to obtain several symmetric properties of the q-Zeta type functions. As applications of these properties, we give some new interesting identities for the modified q-Genocchi polynomials. Finally, our…

Number Theory · Mathematics 2014-09-16 Serkan Araci , Armen Bagdasaryan , Cenap Ozel , H. M. Srivastava

The rapid development of q-calculus has led to the discovery of new generalizations of Bernstein polynomials and Genocchi polynomials involving q-integers. The present paper deals with weighted q-Bernstein polynomials and q-Genocchi numbers…

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

Interpolated multiple $q$-zeta values are deformation of multiple $q$-zeta values with one parameter, $t$, and restore classical multiple zeta values as $t = 0$ and $q \to 1$. In this paper, we discuss generating functions for sum of…

Number Theory · Mathematics 2017-10-12 Zhonghua Li , Noriko Wakabayashi

The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…

Number Theory · Mathematics 2019-07-04 Serkan Araci , Mehmet Acikgoz , Hassan Jolany , Armen Bagdasaryan

In this paper, we construct the alternating multiple q-zeta function(= Multiple Euler q-zeta function) and investigate their properties. Finally, we give some interesting functional eauations related to q-Euler polynomials.

Number Theory · Mathematics 2009-12-31 T. 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 Barnes multiple zeta function is useful to study in the number theory and Knot thoey and Mathematical Physics. In this paper we consider q-extension of Barnes type multiple zeta function and we also construct the q-extension of Euler…

Number Theory · Mathematics 2015-05-14 Taekyun Kim

The main purpose of this paper is to present a systemic study of some families of multiple $q$-Euler numbers and polynomials. In particular, by using the $q$-Volkenborn integration on $\Bbb Z_p$, we construct $p$-adic $q$-Euler numbers and…

Number Theory · Mathematics 2007-05-23 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

We prove nonlinear relation on multiple Hurwitz-Riemann zeta functions. Using analytic continuation of these multiple Hurwitz-Riemann zeta function, we quote at negative integers Euler's nonlinear relation for generalized Bernoulli…

Number Theory · Mathematics 2016-03-15 Abdelmejid Bayad , Takao Komatsu

In this paper we construct $q$-Genocchi numbers and polynomials. By using these numbers and polynomials, we investigate the $q$-analogue of alternating sums of powers of consecutive integers due to Euler.

Number Theory · Mathematics 2007-05-23 Taekyun Kim

The objective of this paper is to derive symmetric property of (h,q)-Zeta function with weight alpha. By using this property, we give some interesting identities for (h,q)-Genocchi polynomials with weight alpha. As a result, our…

Number Theory · Mathematics 2013-08-02 E. Cetin , M. Acikgoz , I. N. Cangul , S. Araci

In this study, we construct the two-variable multiple Dirichlet q-L-function and two-variable multiple Dirichlet type Changhee q-L-function. These functions interpolate the q-Bernoulli polynomials and generalized Changhee q-Bernoulli…

Number Theory · Mathematics 2007-05-23 Y. Simsek , Daeyeoul Kim , Seog-Hoon Rim

The main purpose of this paper is to introduce and investigate a new class of generalized Genocchi polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the Srivastava--Pint\'er addition…

Classical Analysis and ODEs · Mathematics 2012-02-02 Nazim I. Mahmudov

In this paper, we consstruct a new extended q-Bernoulli numbers and poly nomials. From these numbers, we derive the multiple zeta functions and give some relations between multiple Bernoulli numbers and multiple zeta functions.

Number Theory · Mathematics 2007-05-23 Y. Simsek , T. Kim , D. Kim

We define and study the interpolated finite multiple harmonic $q$-series. A generating function of the sums of the interpolated finite multiple harmonic $q$-series with fixed weight, depth and $i$-height is computed. Some Ohno-Zagier type…

Number Theory · Mathematics 2019-03-22 Zhonghua Li , Ende Pan

In this work we derive a bilateral generating function involving the product of an Appell-type product of the Bernoulli and Euler polynomials over independent indices and orders. This function is expressed in terms of the Hurwitz zeta…

General Mathematics · Mathematics 2023-03-01 Robert Reynolds