ON THE q-GENOCCHI NUMBERS AND POLYNOMIALS WITH WEIGHT ZERO AND THEIR APPLICATIONS

Abstract

In the paper, the authors discuss properties of the q-Genocchi numbers and polynomials with weight zero. They discover some interesting relations via the p-adic q-integral on Z_p and familiar basis Bernstein polynomials and show that the p-adic log gamma functions are associated with the q-Genocchi numbers and polynomials with weight zero.