A improving fractional approximation to the Riemann zeta function

Abstract

In this article, we presented an improvement to a locally uniformly approximation of Riemann zeta function, and we found in the numerical results that the approximation using the adjustment we defined gives a lower error in approximation and velocity in reaching the required results, and the domain of convergence in the method presented in this article is greater. We calculated all numerical results using Wolfram Mathematica 10.0.