International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 67, Pages 3631-3652

Shifted quadratic Zeta series

Anthony Sofo

School of Computer Science and Mathematics, Victoria University of Technology, P.O. Box 14428, Victoria 8001, Australia

Received 3 February 2004; Revised 30 June 2004

Copyright © 2004 Anthony Sofo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


It is well known that the Riemann Zeta function ς(p)=n=11/np can be represented in closed form for p an even integer. We will define a shifted quadratic Zeta series as n=11/(4n2α2)p. In this paper, we will determine closed-form representations of shifted quadratic Zeta series from a recursion point of view using the Riemann Zeta function. We will also determine closed-form representations of alternating sign shifted quadratic Zeta series.