We study that the q -Bernoulli polynomials, which were constructed by Kim, are analytic continued to β s ( z ) . A new formula for the q -Riemann zeta function ζ q ( s ) due to Kim in terms of nested series of ζ q ( n ) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an interesting phenomenon of “scattering” of the zeros of β s ( z ) is observed. Following the idea of q -zeta function due to Kim, we are going to use “Mathematica” to explore a formula for ζ q ( n ) .