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Related papers: On the q-extension of higher-order Euler polynomia…

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In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian…

Combinatorics · Mathematics 2012-07-03 Tingyao Xiong , Hung-ping Tsao , Jonathan I. Hall

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

In this paper, we present a new definition and generalization of higher order Daehee of the first and second kind. Some new results for these polynomials and numbers are derived. Furthermore, some interesting special cases of the new…

General Mathematics · Mathematics 2021-03-26 F. M. Abdel Moneim , A. Mustafa , B. S. El-Desouky

The purpose of this paper is to derive some applications of umbral calculus by using extended fermionic p-adic q-integral on Zp. From those applications, we derive some new interesting properties on the new family of Euler numbers and…

Number Theory · Mathematics 2013-09-23 Serkan Araci , Mehmet Acikgoz , Erdoğan Şen

In this paper, we study some symmetric properties of the multiple q-Euler zeta function. From these properties, we derive several identities of symmetry for the (h;q)-extension of higher-order Euler polynomials.

Number Theory · Mathematics 2013-12-17 Dae San Kim , Taekyun Kim

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

The aim of this paper is twofold. The first is to give a quantitative version of Schmidt's subspace theorem for arbitrary families of higher degree polynomials. The second is to give a generalization of the subspace theorem for arbitrary…

Number Theory · Mathematics 2023-08-01 Si Duc Quang

We introduce, characterise and provide a combinatorial interpretation for the so-called $q$-Jacobi-Stirling numbers. This study is motivated by their key role in the (reciprocal) expansion of any power of a second order $q$-differential…

Classical Analysis and ODEs · Mathematics 2015-07-07 Ana F. Loureiro , Jiang Zeng

In this paper we define the generalized q-analogues of Euler sums and present a new family of identities for q-analogues of Euler sums by using the method of Jackson q-integral rep- resentations of series. We then apply it to obtain a…

Number Theory · Mathematics 2017-10-24 Zhonghua Li , Ce Xu

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 purpose of this paper is to introduce and investigate a new unification of unified family of Apostol-type polynomials and numbers based on results given in [24] and [25]. Also, we derive some properties for these polynomials and obtain…

Combinatorics · Mathematics 2014-12-30 B. S. El-Desouky , R. S. Gomaa

The aim of this paper is to derive (by using two operators, representable by a Jacobi matrix) a family of q-orthogonal polynomials, which turn to be dual to alternative q-Charlier polynomials. A discrete orthogonality relation and a…

Classical Analysis and ODEs · Mathematics 2007-05-23 N. M. Atakishiyev , A. U. Klimyk

In this paper, we establish more properties of generalized poly-Euler polynomials with three parameters and we investigate a kind of symmetrized generalization of poly- Euler polynomials. Moreover, we introduce a more general form of multi…

Number Theory · Mathematics 2015-08-11 Hassan Jolany , Roberto B. Corcino

In this paper, we study some symmetric identities of q-Euler numbers and polynomials. From these properties, we derive several identities of q-Euler numbers and polynomials.

Number Theory · Mathematics 2013-10-08 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 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 the present paper, we investigate special generalized q-Euler numbers and polynomials. Some earlier results of T. Kim in terms of q-Euler polynomials with weight alpha can be deduced. For presentation of our formulas we apply the method…

Number Theory · Mathematics 2018-07-23 Serkan Araci , Mehmet Acikgoz , Hassan Jolany

The goal of this article is to invite the reader to get to know and to get involved into higher Teichm\"uller theory by describing some of its many facets.

Geometric Topology · Mathematics 2018-03-20 Anna Wienhard

In this paper, we consider the degenerate Carlitz q-Bernoulli numbers and polynomials and we investigate some properties of those polynomials.

Number Theory · Mathematics 2015-07-20 Taekyun Kim

The aim of the present study is to establish some properties for q-Bessel matrix polynomials such as several q-differential matrix equation, q-differential matrix relations and q-recurrence matrix relations, and integral representation,…

General Mathematics · Mathematics 2025-10-23 Ayman Shehata , M. Tawfik , Ayman M. Mahmoud , Nada Mostafa