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Araci, Serkan,Acikgoz, Mehmet,Park, Kyoung Ho Korean Mathematical Society 2013 대한수학회보 Vol.50 No.2
In this paper, we introduce the $q$-analogue of $p$-adic log gamma functions with weight alpha. Moreover, we give a relationship between weighted $p$-adic $q$-log gamma functions and $q$-extension of Genocchi and Euler numbers with weight alpha.
ANALYTIC CONTINUATION OF WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS
Araci, Serkan,Acikgoz, Mehmet,Gursul, Aynur Korean Mathematical Society 2013 대한수학회논문집 Vol.28 No.3
In the present paper, we analyse analytic continuation of weighted $q$-Genocchi numbers and polynomials. A novel formula for weighted $q$-Genocchi-zeta function $\tilde{\zeta}_{G,q}(s{\mid}{\alpha})$ in terms of nested series of $\tilde{\zeta}_{G,q}(n{\mid}{\alpha})$ is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted $q$-Genocchi polynomials.
A New Family of q-analogue of Genocchi Numbers and Polynomials of Higher Order
Araci, Serkan,Acikgoz, Mehmet,Seo, Jong Jin Department of Mathematics 2014 Kyungpook mathematical journal Vol.54 No.1
In the present paper, we introduce the new generalization of q-Genocchi polynomials and numbers of higher order. Also, we give some interesting identities. Finally, by applying q-Mellin transformation to the generating function for q-Genocchi polynomials of higher order put we define novel q-Hurwitz-Zeta type function which is an interpolation for this polynomials at negative integers.
A NOTE ON THE WEIGHTED TWISTED DIRICHLET'S TYPE q-EULER NUMBERS AND POLYNOMIALS
Araci, Serkan,Aslan, Nurgul,Se, Jong-Jin The Honam Mathematical Society 2011 호남수학학술지 Vol.33 No.3
We in this paper construct Dirichlet's type twisted q-Euler numbers and polynomials with weight ${\alpha}$. We give some interestin identities some relations.
Araci, Serkan,Erdal, Dilek,Kang, Dong-Jin The Honam Mathematical Society 2011 호남수학학술지 Vol.33 No.2
The purpose of this study is to obtain some relations between q-Genocchi numbers and q-Bernstein polynomials by using fermionic p-adic q-integral on $\mathbb{Z}_p$.
Araci, Serkan,Acikgoz, Mehmet The Korean Society for Computational and Applied M 2013 Journal of applied mathematics & informatics Vol.31 No.3
The essential aim of this paper is to define weighted $q$-Hardylittlewood-type maximal operator by means of $p$-adic $q$-invariant distribution on $\mathbb{Z}_p$. Moreover, we give some interesting properties concerning this type maximal operator.
A Note on The Weighted Q-Genocchi Numbers and Polynomials With Their Interpolation Function
( Serkan Araci ),( Mehmet Acikgoz ),( Jong Jin Seo ) 호남수학회 2012 호남수학학술지 Vol.34 No.1
Recently, T. Kim has introduced and analysed the q-Bernoulli numbers and polynomials with weight α cf.[7]: By the same motivaton, we also give some interesting properties of the q-Genocchi numbers and polynomials with weight α Also, we derive the q-extensions of zeta type functions with weight α from the Mellin transformation of this generating function which interpolates the q-Genocchi polynomials with weight α at negative integers.
A Note on the Weighted Twisted Dirichlet`s Type Q-Euler Numbers and Polynomials
( Serkan Araci ),( Nurgul Aslan ),( Jong Jin Seo ) 호남수학회 2011 호남수학학술지 Vol.33 No.3
We in this paper construct Dirichlet`s type twisted q-Euler numbers and polynomials with weight a. We give some interesting identities some relations.
Some New Properties On The q-Genocchi Numbers and Polynomials Associated With q-Bernstein Polyomials
( Serkan Araci ),( Dilek Erdal ),( Dong Jin Kang ) 호남수학회 2011 호남수학학술지 Vol.33 No.2
The purpose of this study is to obtain some relationsbetween q-Genocchi numbers and q-Bernstein polynomials by usingfermionic p-adic q-integral on Zp.
A note on the Frobenius-Euler numbers and polynomials associated with Bernstein polynomials
S. Araci,M. Acikgoz 장전수학회 2012 Advanced Studies in Contemporary Mathematics Vol.22 No.3
The present paper deals with Bernstein polynomials and Frobenius-Euler numbers and polynomials. We apply the method of generating function and fermionic p-adic integral representation on Z_p, which are exploited to derive further classes of Bernstein polynomials and Frobenius-Euler numbers and polynomials. To be more precise we summarize our results as follows,we obtain some combinatorial relations between Frobenius-Euler numbers and polynomials. Furthermore, we derive an integral representation of Bernstein polynomials of degree n on Z_p. Also we deduce a fermionic p-adic integral rep-resentation of product Bernstein polynomials of di¤erent degrees n_1, n_2 ,... on Z_p and show that it can be written with Frobenius-Euler numbers which yields a deeper insight into the e¤ectiveness of this type of generalizations. Our applications possess a number of interesting properties which we state in this paper.