Analytic continuation of weighted q-genocchi numbers and polynomials

Abstract

In the present paper, we analyse analytic continuation of weighted q-Genocchi numbers and polynomials. A novel formula for weighted q-Genocchi-zeta function ζG,q (s | α) in terms of nested series of ζG,q (n | α) is derived. Moreover, we introduce a novel concept of dy-namics of the zeros of analytically continued weighted q-Genocchi poly-nomials. © 2013 The Korean Mathematical Society.