Journal of Applied Mathematics
Volume 2012 (2012), Article ID 743939, 8 pages
http://dx.doi.org/10.1155/2012/743939
Research Article

On the 𝑞 -Genocchi Numbers and Polynomials with Weight 𝛼 and Weak Weight 𝛽

J. Y. Kang, H. Y. Lee, and N. S. Jung

Department of Mathematics, Hannam University, Daejeon 306-791, Republic of Korea

Received 20 November 2011; Accepted 19 February 2012

Academic Editor: Francis T. K. Au

Copyright © 2012 J. Y. Kang 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

We construct a new type of 𝑞 -Genocchi numbers and polynomials with weight 𝛼 and weak weight 𝛽 ∶ 𝐺 ( 𝛼 , 𝛽 ) 𝑛 , 𝑞 , 𝐺 ( 𝛼 , 𝛽 ) 𝑛 , 𝑞 ( 𝑥 ) , respectively. Some interesting results and relationships are obtained.