Evaluation of Riemann Zeta function on the Line $\Re(s) = 1$ and Odd Arguments

Abstract

We have looked at the evaluation of the Riemann Zeta function at odd arguments and have provided a simple formula to approximate the value with exponential convergence. We have compared it with various other formulae present in literature. We have also evaluated an expression for the zeta function on the plane $\Re(s) = 1$.