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- Serkan Araci, Dilek Erdal, Jong Jin Seo
- 2014

and Applied Analysis 3 2. On the Weighted q-Genocchi Numbers and Polynomials By the definition of q-Genocchi polynomials with weight α, we easily get

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
- Applied Mathematics and Computation
- 2014

and Applied Analysis 3 Similarly, the q-Bernoulli polynomials and numbers with weight 0 are defined, respectively, as B̃n,q x lim n→∞ 1 [ pn ] q pn−1 ∑ y 0 ( x y )n q

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

- 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 polynomials with weight α . We apply the method of generating function and p -adic q -integral representation on Zp , which are exploited to derive further classes of q -Euler numbers and polynomials. Our new generating function possess a number of interesting properties which… (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, Mehmet Açikgöz, Cenap Özel, Hari M. Srivastava, Toka Diagana
- Int. J. Math. Mathematical Sciences
- 2015

- Serkan Araci, Waseem A. Khan, Mehmet Acikgoz, Cenap Özel, Poom Kumam
- SpringerPlus
- 2016

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)

- Serkan Araci, Mehmet Açikgöz, Erdogan Sen
- Int. J. Math. Mathematical Sciences
- 2014