Advances in Difference Equations
Volume 2008 (2008), Article ID 195049, 14 pages
doi:10.1155/2008/195049
On some arithmetical properties of the Genocchi numbers and polynomials
Kyoung Ho Park1
and Young-Hee Kim2
1Department of Mathematics, Kyungpook National University, Daegu 702-701, South Korea
2Division of General Education-Mathematics, Kwangwoon University, Seoul 139-701, South Korea
Abstract
We investigate the properties of the Genocchi functions and the Genocchi polynomials. We obtain the Fourier transform on the Genocchi function. We have the generating function of (h,q)-Genocchi polynomials. We define the Cangul-Ozden-Simsek's type twisted (h,q)-Genocchi polynomials and numbers. We also have the generalized twisted (h,q)-Genocchi numbers attached to the Dirichlet's character χ. Finally, we define zeta functions related to (h,q)-Genocchi polynomials and have the generating function of the generalized (h,q)-Genocchi numbers attached to χ.