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- 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)

- Armen Bagdasaryan, Serkan Araci, Mehmet Acikgoz, Yuan He
- 2016

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)

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, Xiangxing Kong, Mehmet Acikgoz, Erdo Gan, S en
- 2013

We derive numerous identities for multivariate q-Euler polynomials by using the umbral calculus.