Discrete Dynamics in Nature and Society
Volume 2011 (2011), Article ID 487490, 7 pages
http://dx.doi.org/10.1155/2011/487490
Research Article

New Construction Weighted ( ℎ , 𝑞 ) -Genocchi Numbers and Polynomials Related to Zeta Type Functions

Serkan Araci,1 Jong Jin Seo,2 and Dilek Erdal1

1Department of Mathematics, Faculty of Arts and Science, University of Gaziantep, 27310 Gaziantep, Turkey
2Department of Applied Mathematics, Pukyong National University, Busan 608-737, Republic of Korea

Received 31 March 2011; Revised 17 June 2011; Accepted 11 July 2011

Academic Editor: Guang Zhang

Copyright © 2011 Serkan Araci 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.

Abstract

The fundamental aim of this paper is to construct ( ℎ , 𝑞 ) -Genocchi numbers and polynomials with weight 𝛼 . We shall obtain some interesting relations by using 𝑝 -adic 𝑞 -integral on ℤ 𝑝 in the sense of fermionic. Also, we shall derive the ( ℎ , 𝑞 ) -extensions of zeta type functions with weight 𝛼 from the Mellin transformation of this generating function which interpolates the ( ℎ , 𝑞 ) -Genocchi numbers and polynomials with weight 𝛼 at negative integers.