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