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 dynamics of the zeros of analytically continued weighted q-Genocchi polynomials.

5 pages, submitted

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