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Related papers: On the multiple q-Genocchi and Euler numbers

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One purpose of this paper is to construct twisted q-Euler numbers by using p-adic invariant integral on Zp in the sense of fermionic. Finally, we consider twisted Euler q-zeta function and q-l-series which interpolate twisted q-Euler…

Number Theory · Mathematics 2015-06-26 T. Kim , S. H. Rim

In the present paper, we propose the modified q-Bernstein polynomials of degree n, which are different q-Bernstein polynomials of Phillips(see [4]). From these the modified q-Bernstein polynomials of degree n, we derive some interesting…

Number Theory · Mathematics 2010-05-25 Taekyun Kim , Lee-Chae Jang , Heungsu Yi

We realize that geometric polynomials and p-Bernoulli polynomials and numbers are closely related with an integral representation. Therefore, using geometric polynomials, we extend some properties of Bernoulli polynomials and numbers such…

Number Theory · Mathematics 2017-02-22 Levent Kargın

We study the explicit formula of Euler numbers and polynomials of higher order

Number Theory · Mathematics 2007-05-23 Taekyun Kim

In the present paper, we analyse analytic continuation of weighted q-Genocchi numbers and polynomials. A novel formula for weighted q-Genocchi- Zeta function {\zeta}G,q (s | {\alpha}) in terms of nested series of {\zeta}G,q (n | {\alpha})…

Number Theory · Mathematics 2013-08-14 Serkan Araci , Mehmet Acikgoz , Aynur Gursul

In this paper, we investigate the properties of symmetry in two variables related to multiple Euler q-l-function which interpolates higher-order q-Euler polynomials at negative integers. From our investigation, we can derive many…

Number Theory · Mathematics 2013-12-18 D. V. Dolgy , D. S. Kim , T. G. Kim , J. J. Seo

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 note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…

Combinatorics · Mathematics 2016-03-01 Beáta Bényi , Péter Hajnal

In this we give a detailed proof of fermionic p-adic q-measures on Z_p and we will treat some interesting formulae related q-extension of Euler numbers and polynomials.

Number Theory · Mathematics 2007-07-02 Taekyun Kim

The aim of this paper is to present a general algebraic identity. Applying this identity, we provide several formulas involving the q-binomial coefficients and the q-harmonic numbers. We also recover some known identities including an…

Combinatorics · Mathematics 2023-02-01 Said Zriaa , Mohammed Mouçouf

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

it is the purpose of this paper to construct a p-adic continuous function for an odd prime to contain a p-adic q-analogue of higher order Dedekind type sums related to q-Euler polynomials and numbers.

Number Theory · Mathematics 2009-07-30 T. Kim

In this paper, we introduce bivariate polynomial sets of deformed $q$-Appell type, and we study the algebraic properties of these sets. We show the relation between deformed bivariate $q$-Appell polynomials and deformed homogeneous…

Combinatorics · Mathematics 2025-05-29 Ronald Orozco López

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

Certain generalization of Euler numbers was defined in 1935 by Lehmer using cubic roots of unity, as a natural generalization of Bernoulli and Euler numbers. In this paper, we define a new polynomial related to the higher-order generalized…

Combinatorics · Mathematics 2025-07-24 Wei-Wei Qi

In this paper we construct the q-analogue of Barnes' Bernoulli numbers and plynomials of degree 2, which is an answer to a part of Schlosser's question. Finally, we treat the q-analogue of the sums of powers of consecutive integrs.

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

In the recent p-adic q-integral on the p-adic integers' rings was constructed >. The purpose of this paper is to give several interesting integral equation for the p-adic q-integerals on the rings of p-adic integers. As an integral…

Number Theory · Mathematics 2007-05-23 Taekyun Kim

We introduce a new generalization of Euler's $\varphi$-function associated with a system of polynomials of several variables. We reprove by a short direct approach certain known related identities, and study some other special cases that do…

Number Theory · Mathematics 2025-08-27 Norbert Csizmazia , László Tóth

A combinatorial study of multiple $q$-integrals is developed. This includes a $q$-volume of a convex polytope, which depends upon the order of $q$-integration. A multiple $q$-integral over an order polytope of a poset is interpreted as a…

Combinatorics · Mathematics 2016-08-12 Jang Soo Kim , Dennis Stanton

In this paper we constructed new q-extension of Bernstein polynomials. Fron those q-Berstein polynomials, we give some interesting properties and we investigate some applications related this q-Bernstein polynomials.

Number Theory · Mathematics 2015-05-19 Taekyun Kim