Riemann Zeta Function. Chi(s)via analytic Continuation inside an infinite Loop
Number Theory
2013-12-12 v2
Abstract
The paper deals with the analytic entire function Chi(s) closely related to Riemann Zeta Function Zeta(s). A formula is obtained for Chi(s) essentially within the so-called critical strip. This is achieved by applying Cauchy integral formula to an infinite loop encircling the critical strip. In the obtained formula a remarkable role is played by a special type of complex function known as Incomplete Gamma Function. Numerical examples verifying the obtained formula are included.
Cite
@article{arxiv.1312.2890,
title = {Riemann Zeta Function. Chi(s)via analytic Continuation inside an infinite Loop},
author = {Renaat Van Malderen},
journal= {arXiv preprint arXiv:1312.2890},
year = {2013}
}