Calculating zeros of the \(q\)-Genocchi polynomials associated with \(p\)-adic \(q\)-integral on \(\mathbb Z_p\) (Q715114)

Summary: In this paper we construct the new analogues of Genocchi the numbers and polynomials. We also observe the behavior of complex roots of the \(q\)-Genocchi polynomials \(G_{n,q}(x)\), using numerical investigation. By means of numerical experiments, we demonstrate a remarkably regular structure of the complex roots of the \(q\)-Genocchi polynomials \(G_{n,q}(x)\). Finally, we give a table for the solutions of the \(q\)-Genocchi polynomials \(G_{n,q}(x)\).