New construction of weighted \((h, q)\)-Genocchi numbers and polynomials related to zeta type functions (Q659520)

Summary: The fundamental aim of this paper is to construct \((h, q)\)-Genocchi numbers and polynomials with weight \(\alpha\). We obtain certain relations by using a fermionic \(p\)-adic \(q\)-integral on \(\mathbb Z_p\). Also, we derive the \((h, q)\)-extensions of zeta type functions with weight \(\alpha\) from the Mellin transformation of this generating function which interpolates the \((h, q)\)-Genocchi numbers and polynomials with weight \(\alpha\) at negative integers.