Exploring the q -Riemann zeta function and q -Bernoulli polynomials

T. Kim, C. S. Ryoo, L. C. Jang and S. H. Rim

Discrete Dynamics in Nature and Society, 2005, vol. 2005, 1-11

Abstract:

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 ) .

Date: 2005
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnddns:816261

DOI: 10.1155/DDNS.2005.171

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