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Exploring the q-Riemann zeta function and q-Bernoulli polynomials
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| DISCRETE DYNAMICS IN NATURE AND SOCIETY |
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We study the q-Bernoulli polynomials, which were constructed by Kim, are analytic continued to beta(s)(z). A new formula for the q-Riemann zeta function zeta(q)(s) due to Kim in terms of nested series of zeta(q)(n) is derived. The new concept of dynamics of zeros of analytic continued polynomials is introduced, and an interesting phenomenon of "scattering" of the zeros of beta(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 zeta(q)(n).
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q-Bernoulli polynomials, q-Riemann zeta function, nested series, q-extension
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