The Consequence of the Analytic Continuity of Zeta Function Subject to an Additional Term and a Justification of the Location of the Non-Trivial Zeros

We review two main results of Riemann Zeta function; the analytic continuity and the first functional equation by the means of Gamma function and Hankel contour. We observe that an additional term is considered in both results. We justify the non-trivial location of Zeta non-trivial zeros subject to an approximation.