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In [14] Ozden-Simsek-Cangul constructed generating functions of higher-order twisted $(h,q)$-extension of Euler polynomials and numbers, by using $p$-adic q-deformed fermionic integral on $\Bbb Z_p$. By applying their generating functions,…

Number Theory · Mathematics 2007-11-01 Taekyun Kim , Leechae Jang , Cheon-Seoung Ryoo

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

The main purpose of this paper is to introduce and investigate a class of generalized Bernoulli polynomials and Euler polynomials based on the generating function. we unify all forms of q-exponential functions by one more parameter. we…

Complex Variables · Mathematics 2018-10-24 N. I. Mahmudov , Mohammad Momenzadeh

In the present article, we introduce a $(p,q)$-analogue of the poly-Euler polynomials and numbers by using the $(p,q)$-polylogarithm function. These new sequences are generalizations of the poly-Euler numbers and polynomials. We give…

Number Theory · Mathematics 2016-04-14 Takao Komatsu , José L. Ramírez , Víctor F. Sirvent

In this paper we construct the $q$-analogue of Barnes's Bernoulli numbers and polynomials of degree 2, for positive even integers, which is an answer to a part of Schlosser's question. For positive odd integers, Schlosser's question is…

Number Theory · Mathematics 2016-09-07 Y. Simsek , D. Kim , T. Kim , S. H. Rim

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

In this paper, we will study p-adic q-expansion of alternating sums of powers. From these properties, we derive some interesting properties related to p-adic q-expansion of alternating sums of powers

Number Theory · Mathematics 2007-05-23 Taekyun Kim

We consider summation of some finite and infinite functional p-adic series with factorials. In particular, we are interested in the infinite series which are convergent for all primes p, and have the same integer value for an integer…

Number Theory · Mathematics 2014-11-18 Branko Dragovich , Natasa Z. Misic

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

Finite trigonometric sums appear in various branches of Physics, Mathematics and their applications. For p; q to coprime positive integers and r we consider the finite trigonometric sums involving the product of three trigonometric…

Number Theory · Mathematics 2018-11-02 Mouloud Goubi

The main purpose of this paper is to introduce and investigate a new class of generalized Bernoulli polynomials and Euler polynomials based on the q-integers. The q-analogues of well-known formulas are derived. The q-analogue of the…

Classical Analysis and ODEs · Mathematics 2012-02-01 Nazim I. Mahmudov

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

Many mathematicians have been studying various degenerate versions of special polynomials and numbers in some arithmetic and combinatorial aspects. Our main focus here is a new type of degenerate poly-Euler polynomials and numbers. This…

Combinatorics · Mathematics 2022-10-19 Yuankui Ma , Taekyun Kim , Hongze Li

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

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 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 study a new p-adic q-l-functions and sums of powers.

Number Theory · Mathematics 2007-05-23 Taekyun Kim

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 paper, we derive basic identities of symmetry in two variables related to higher-order q-Euler polynomials and q-analogue of higher order alternating power sums. The derivation of identities are based on the multibvariate p-adic…

Number Theory · Mathematics 2014-01-14 Dae San Kim , Taekyun Kim

The aim of this paper is twofold. Firstly, we investigate a finite sum involving the generalized falling factorial polynomials, in some special cases of which we express it in terms of the degenerate Stirling numbers of the second kind, the…

Number Theory · Mathematics 2023-01-11 Taekyun Kim , Dae San Kim