Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Review Article q-Genocchi Numbers and Polynomials Associated with q-Genocchi-Type l-Functions | Hindawi Publishing Corporation Advances in Difference Equations Volume 2008 Article ID 815750 12 pages doi 2008 815750 Review Article q-Genocchi Numbers and Polynomials Associated with q-Genocchi-Type -Functions Yilmaz Simsek 1 Ismail Naci Cangul 2 Veli Kurt 1 and Daeyeoul Kim3 1 Department of Mathematics Faculty of Arts and Science University ofAkdeniz Antalya 07058 Turkey 2 Department of Mathematics Faculty of Arts and Science University ofUludag Bursa 16059 Turkey 3 National Institute for Mathematical Sciences Doryong-dong Yuseong-gu Daejeon 305-340 South Korea Correspondence should be addressed to Yilmaz Simsek ysimsek@ Received 19 March 2007 Accepted 14 December 2007 Recommended by Rigoberto Medina 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 -functions which are interpolated q-Genocchi numbers and polynomials at negative integers. We also give some applications of the generalized q-Genocchi numbers. Copyright 2008 Yilmaz Simsek et al. This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited. 1. Introduction definitions and notations In 1 Jang et al. gave new formulae on Genocchi numbers. They defined poly-Genocchi numbers to give the relation between Genocchi numbers Euler numbers and poly-Genocchi numbers. In 2 Kim et al. constructed new generating functions of the q-analogue Eulerian numbers and q-analogue Genocchi numbers. They gave relations between Bernoulli numbers Euler numbers and Genocchi numbers. They also defined Genocchi zeta functions which interpolate these numbers at .
