• 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)
  • Received : 2012.10.11
  • Published : 2013.07.31


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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