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

Abstract

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.

8 pages

Cited by in corpus (2)

• Some New Identities of Genocchi Numbers and Polynomials involving Bernoulli and Euler polynomials
• On the Dirichlet's type of Eulerian polynomials