Mathematica 9 is now available

Wolfram Library Archive


Courseware Demos MathSource Technical Notes
All Collections Articles Books Conference Proceedings
Title

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

T Kim
CS Ryoo
LC Jang
SH Rim
Journal / Anthology

DISCRETE DYNAMICS IN NATURE AND SOCIETY
Year: 2005
Volume: 2
Page range: 171-181
Description

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).
Subject

*Mathematics > Calculus and Analysis > Special Functions
Keywords

q-Bernoulli polynomials, q-Riemann zeta function, nested series, q-extension