Some relations of the twisted \(q\)-Genocchi numbers and polynomials with weight \(\alpha\) and weak weight \(\beta\) (Q437649)

Summary: 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.