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A NEW CONSTRUCTION ON THE DEGENERATE HURWITZ-ZETA FUNCTION ASSOCIATED WITH CERTAIN APPLICATIONS
M. SELÇUK AYDIN,MEHMET ACIKGOZ,SERKAN ARACI 장전수학회 2022 Proceedings of the Jangjeon mathematical society Vol.25 No.2
In [5], Kim and Kim de fined degenerate version of gamma functions, and then introduced its new properties by making use of analytical methods in the complex analysis. With this in mind, we consider the degenerate Hurwitz-zeta, modi fied degenerate Hurwitz- zeta, degenerate digamma functions. We obtain several new properties and identities for these functions.
SYMMETRIC IDENTITIES INVOLVING WEIGHTED q-GENOCCHI POLYNOMIALS UNDER S4
U. Duran,M. Acikgoz,S. Araci 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.4
In the paper, we obtain some new symmetric identities of weighted q-Genocchi polynomials using the fermionic p-adic q-integral on Zp.
A symmetric identity on the q-Genocchi polynomials of higher-order under third dihedral group D3
E. Agyüz,M. Acikgoz,S. Araci 장전수학회 2015 Proceedings of the Jangjeon mathematical society Vol.18 No.2
In the present paper, we perform a further investigation for the q-Genocchi numbers and polynomials of higher order under third Dihedral group D3 and establish some closed formulae of the symmetric identities. We also establish some known identities for the classical Genocchi numbers and polynomials by using fermionic p-adic 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.
Identities involving the -Genocchi polynomials and -Zeta-type function
A. Bagdasaryan,E.Sen,Y.He,S. Araci,M. Acikgoz 장전수학회 2014 Advanced Studies in Contemporary Mathematics Vol.24 No.2
The fundamental objective of this paper is to obtain some interesting properties for (h,q)-Genocchi numbers and polynomials by using the fermionic p-adic q-integral on Zp and mentioned in the paper q-Bernstein polynomials. By applying the Mellin transformation to the generating function of (h,q)-Genochhi polynomials, we define (h,q)-Zeta-type function. Moreover, we derive symmetric properties of (h,q)-Zeta funtion and from these properties we give symmetric property of (h,q)-Genocchi polynomials.