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In this paper we study that the q-Bernoulli polynomial, which were constructed by T.Kim, are analytic continued to βs(z). A new formula for the q-Riemann Zeta function ζ,(s) due to T.Kim (see [1,2,8]) in terms of nested series of ζ,(n) is derived. The new concept of dynamics of the zeros of analytic continued polynomials is introduced, and an investing phenomenon of ‘scattering’ of the zeros of βs(z) is observed. Following the idea of q-zeta function due to T.Kim, we are going to use “Mathematica” to explore a formula for ζ,(n).
- q-Bernoulli polynomial
- q-Riemann Zeta function
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Cite this paper
Kim, T., Ryoo, C. S., Jang, L. C., and Rim, S. K. (2005). Exploring the q-Riemann Zeta function and q-Bernoulli polynomials. Notes on Number Theory and Discrete Mathematics, 11(1), 7-19.