Advances in Difference Equations
Volume 2008 (2008), Article ID 195049, 14 pages
doi:10.1155/2008/195049
Research Article

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

Received 31 October 2008; Revised 19 December 2008; Accepted 25 December 2008

Academic Editor: Martin J. Bohner

Copyright © 2008 Kyoung Ho Park and Young-Hee 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.

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.