Abstract and Applied Analysis
Volume 2008 (2008), Article ID 232187, 8 pages
doi:10.1155/2008/232187
q-Genocchi Numbers and Polynomials Associated with Fermionic p-Adic Invariant Integrals on ℤp
Leechae Jang1
and Taekyun Kim2
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
Abstract
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 p-adic invariant integral on ℤp, we construct p-adic Genocchi numbers and polynomials of higher order. Finally, we derive the following interesting formula: Gn+k,q(k)(x)=2kk!(n+kk)∑l=0∞∑d0+d1+⋯+dk=k−1,di∈ℕ(−1)l(l+x)n, where Gn+k,q(k)(x) are the q-Genocchi polynomials of order k.