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- Mehmet Açikgöz, Dilek Erdal, Serkan Araci
- 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
- 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)

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)

In the present paper, we introduce a method in order to obtain some new interesting relations and identities of the Apostol-Bernoulli polynomials of higher order, which are derived from Bernoulli polynomial basis. Finally, by utilizing this method, we also get formulas for the convolutions of Bernoulli and Euler polynomials in terms of Apostol-Bernoulli… (More)

- Serkan Araci, Mehmet Acikgoz, Erdo Gan S ¸en
- 2014

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)

- Serkan Araci, Mehmet Acikgoz, Kyoung-Ho Park, Hassan Jolany
- 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)

By using the modified Milne-Thomson's polynomial given in Araci et al. (Appl Math Inf Sci 8(6):2803-2808, 2014), we introduce a new concept of the Apostol Hermite-Genocchi polynomials. We also perform a further investigation for aforementioned polynomial and derive some implicit summation formulae and general symmetric identities arising from different… (More)