Advances in Difference Equations 
Volume 2008 (2008), Article ID 815750, 12 pages
doi:10.1155/2008/815750
Review Article

q-Genocchi Numbers and Polynomials Associated with q-Genocchi-Type l-Functions

Yilmaz Simsek,1 Ismail Naci Cangul,2 Veli Kurt,1 and Daeyeoul Kim3

 1Department of Mathematics, Faculty of Arts and Science, University of Akdeniz, Antalya 07058, Turkey
2Department of Mathematics, Faculty of Arts and Science, University of Uludag, Bursa 16059, Turkey
3National Institute for Mathematical Sciences, Doryong-dong, Yuseong-gu, Daejeon 305-340, South Korea
Received 19 March 2007; Accepted 14 December 2007

Recommended by Rigoberto Medina

Abstract

The main purpose of this paper is to study generating functions of the q-Genocchi numbers and polynomials. We prove a new relation for the generalized q-Genocchi numbers, which is related to the q-Genocchi numbers and q-Bernoulli numbers. By applying Mellin transformation and derivative operator to the generating functions, we define q-Genocchi zeta and l-functions, which are interpolated q-Genocchi numbers and polynomials at negative integers. We also give some applications of the generalized q-Genocchi numbers.