Riemann's Zeta Function. Numerical Evaluation via its Alternating Relative \eta(s)

Abstract

The paper describes a method for calculating values of Riemann's Zeta function within the critical strip 0< {\sigma} <1 and on its boundary. The approach is based on the "Alternating Zeta function" {\eta}(s). The actual Riemann Zeta function {\zeta}(s) is easily obtained from {\eta}(s). The obtained accuracy, within certain limits of the described method is discussed. A decent scientific calculator suffices to carry out the involved computations.