# ANALYTIC CONTINUATION OF WEIGHTED q-GENOCCHI NUMBERS AND POLYNOMIALS

• Araci, Serkan (Department of Mathematics Faculty of Arts and Science University of Gaziantep) ;
• Acikgoz, Mehmet (Department of Mathematics Faculty of Arts and Science University of Gaziantep) ;
• Gursul, Aynur (Department of Mathematics Faculty of Arts and Science University of Gaziantep)
• Published : 2013.07.31

#### 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 $\tilde{\zeta}_{G,q}(s{\mid}{\alpha})$ in terms of nested series of $\tilde{\zeta}_{G,q}(n{\mid}{\alpha})$ is derived. Moreover, we introduce a novel concept of dynamics of the zeros of analytically continued weighted $q$-Genocchi polynomials.

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#### Cited by

1. A New Family of q-analogue of Genocchi Numbers and Polynomials of Higher Order vol.54, pp.1, 2014, https://doi.org/10.5666/KMJ.2014.54.1.131
2. On the families of q-Euler polynomials and their applications vol.23, pp.1, 2015, https://doi.org/10.1016/j.joems.2014.03.002