On the $q$-Genocchi numbers and polynomials with weight zero and their applications

Serkan Araci, Mehmet Acikgoz, Feng Qi

Published 2012-02-13Version 1

In this paper, the authors deal with the $q$-Genocchi numbers and polynomials with weight zero. They discover some interesting relations via the $p$-adic $q$-integral on $\mathbb{Z}_{p}$ and familiar basis Bernstein polynomials. Finally, the authors show that the $p$-adic $\log$ gamma functions are associated with the $q$-Genocchi numbers and polynomials with weight zero.