Advances in Difference Equations
Volume 2011 (2011), Article ID 424809, 8 pages
doi:10.1155/2011/424809
Review Article

On the Generalized 𝑞 -Genocchi Numbers and Polynomials of Higher-Order

C. S. Ryoo,1 T. Kim,2 J. Choi,2 and B. Lee3

1Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea
2Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea
3Department of Wireless Communications Engineering, Kwangwoon University, Seoul 139-701, Republic of Korea

Received 10 August 2010; Accepted 18 February 2011

Academic Editor: Roderick Melnik

Copyright © 2011 C. S. Ryoo 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.

Abstract

We first consider the 𝑞 -extension of the generating function for the higher-order generalized Genocchi numbers and polynomials attached to 𝜒 . The purpose of this paper is to present a systemic study of some families of higher-order generalized 𝑞 -Genocchi numbers and polynomials attached to 𝜒 by using the generating function of those numbers and polynomials.