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- Yuan He, Serkan Araci, Hari M. Srivastava, Mehmet Açikgöz
- Applied Mathematics and Computation
- 2015

- Mehmet Açikgöz, Dilek Erdal, Serkan Araci, Claudio Cuevas
- 2011

Copyright q 2010 Mehmet Açikgöz et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. We present a new generating function related to the q-Bernoulli numbers and q-Bernoulli polynomials. We… (More)

- SERKAN ARACI, MEHMET ACIKGOZ, HASSAN JOLANY, Kurt Hensel, H. JOLANY
- 2012

In the present paper, we introduce modified Dirichlet's type of twisted q-Euler poly-nomials with weight α. We apply the method of generating function and p-adic q-integral representation on Z p , which are exploited to derive further classes of q-Euler numbers and polynomials. Our new generating function possess a number of interesting properties which we… (More)

- Serkan Araci, Mehmet Açikgöz, Erdogan Sen
- Applied Mathematics and Computation
- 2014

Keywords: Genocchi numbers and polynomials q-Genocchi numbers von Staudt–Clausen's theorem Kummer congruence a b s t r a c t Recently, the von Staudt–Clausen's theorem for q-Euler numbers was introduced by Kim (2013) and q-Genocchi numbers were constructed by Araci et al. (2013). In this paper, we give the corresponding von Staudt–Clausen's theorem for… (More)

- Serkan Araci
- Applied Mathematics and Computation
- 2014

- SERKAN ARACI, MEHMET ACIKGOZ, KYOUNG-HO PARK, HASSAN JOLANY, Kurt Hensel
- 2012

The present paper deals with uni…cation of the multiple twisted Euler and Genocchi numbers and polynomials associated with p-adic q-integral on Zp at q = 1. Some earlier results of Ozden's papers in terms of uni…ca-tion of the multiple twisted Euler and Genocchi numbers and polynomials associated with p-adic q-integral on Zp at q = 1 can be deduced. We… (More)

In the present paper, we introduce Eulerian polynomials with parameters a and b and give the definition of them. By using the definition of generating function for our polynomials, we derive some new identities in Analytic Numbers Theory. Also, we give relations between Eulerian polynomials with parameters a and b, Bernstein polynomials, Poly-logarithm… (More)

- Mehmet Açikgöz, Serkan Araci, Ismail Naci Cangül
- Applied Mathematics and Computation
- 2011

- Serkan Araci, Mehmet Acikgoz, Hassan Jolany, Yuan He
- 2014

In this paper, we focus on the q-Genocchi numbers and polynomials. We introduce new identities of the q-Genocchi numbers and polynomials by using the fermionic p-adic integral on Z p. Also, we give Cauchy-integral formula for the q-Genocchi polynomials and derive the distribution formula q-Genocchi polynomials by using measure theory on p-adic integral.… (More)

- Serkan Araci, Erdogan Sen
- Ars Comb.
- 2015