Some Relations of the Twisted q-Genocchi Numbers and Polynomials with Weight α and Weak Weight β

Abstract

Recently many mathematicians are working on Genocchi polynomials and Genocchi numbers. We define a new type of twisted q-Genocchi numbers and polynomials with weight $\alpha$ and weak weight $\beta$ and give some interesting relations of the twisted q-Genocchi numbers and polynomials with weight $\alpha$ and weak weight $\beta$. Finally, we find relations between twisted q-Genocchi zeta function and twisted Hurwitz q-Genocchi zeta function.