In this paper we construct a new type of twisted q-Genocchi numbers and polynomials with weak weight α. We investigate some properties which are related to twisted q-Genocchi numbers G (α) n,q,w and polynomials G (α) n,q,w (x) with weak weight α. Keywords: Genocchi numbers and polynomials, twisted q-Genocchi numbers and polynomials, twisted q-Genocchi numbers and polynomials with weak weight α

We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function.We have the generating function of h, q -Genocchi polynomials. We define the Cangul-Ozden-Simsek’s type twisted h, q -Genocchi polynomials and numbers. We also have the generalized twisted h, q -Genocchi numbers attached to the Dirichlet’s character χ. F...

In this paper we construct the new analogues of Genocchi the numbers and polynomials. We also observe the behavior of complex roots of the q-Genocchi polynomials Gn,q x , using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the q-Genocchi polynomials Gn,q x . Finally, we give a table for the solutions of the q-Ge...

In this paper, we define the Apostol-Genocchi polynomials and qApostol-Genocchi polynomials. We give the generating function and some basic properties of q-Apostol-Genocchi polynomials. Several interesting relationships are also obtained. 2000 Mathematics Subject Classification: Primary 05A30; Secondary 11B83, 11M35, 33E20.

Recently, many mathematicians have studied various kinds of the q-analogue of Genocchi numbers and polynomials. In the work New approach to q-Euler, Genocchi numbers and their interpolation functions, “Advanced Studies in Contemporary Mathematics, vol. 18, no. 2, pp. 105– 112, 2009.”, Kim defined new generating functions of q-Genocchi, q-Euler polynomials, and their interpolation functions. In ...

tributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract Our aim in this paper is to discover special symmetric properties for twisted q-Genocchi polynomials. We are going to find a symmetric identity for twisted q-Genocchi zeta function. From property of the twis...

We investigate some algorithms that produce Bernoulli, Euler and Genocchi polynomials. We also give closed formulas for Bernoulli, Euler and Genocchi polynomials in terms of weighted Stirling numbers of the second kind, which are extensions of known formulas for Bernoulli, Euler and Genocchi numbers involving Stirling numbers of the second kind.

Cangul-Ozden-Simsek[1] constructed the q-Genocchi numbers of high order using a fermionic p-adic integral on Zp, and gave Witt’s formula and the interpolation functions of these numbers. In this paper, we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers of Cangul-Ozden-Simsek. We define q-extensions of w-Euler numbers and polynomials, and w-Genocchi numbers ...

The present paper deals with the various q-Genocchi numbers and polynomials. We define a new type ofmultiple generalized q-Genocchi numbers and polynomials withweight α andweakweight β by applying the method of p-adic q-integral. We will find a link between their numbers and polynomials with weight α and weak weight β. Also we will obtain the interesting properties of their numbers and polynomi...

In this paper, we introduce a new type of degenerate Genocchi polynomials and numbers, which are called poly-Genocchi by using the polylogarithm function, derive several properties these systematically. Then, also consider unipoly-Genocchi attached to an arithmetic investigate some identities those polynomials. particular, give explicit expressions unipoly related special numbers