Abstract and Applied Analysis
Volume 2008 (2008), Article ID 232187, 8 pages
-Genocchi Numbers and Polynomials Associated with Fermionic -Adic Invariant Integrals on
1Department of Mathematics and Computer Science, KonKuk University, Chungju 380-701, South Korea
2Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, South Korea
Received 3 April 2008; Accepted 22 April 2008
Academic Editor: Ferhan Atici
Copyright © 2008 Leechae Jang and Taekyun Kim. 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.
The main purpose of this paper is to present a systemic study of some
families of multiple Genocchi numbers and polynomials. In particular, by using the
fermionic -adic invariant integral on , we construct -adic Genocchi numbers and
polynomials of higher order. Finally, we derive the following interesting formula: , where are the -Genocchi polynomials of order .