Proof of Bernhard Riemann's Functional Equation using Gamma Function

Abstract

This study shows the use of gamma function to prove the Riemann functional equation. Two approaches had been used to solve this problem: first the value of t in the definition of the gamma function had been changed to pi nu x if only if sigma is greater than zero in the complex plane. Secondly, the Poisson summation formula is used to show that zeta has a simple pole at s = 1 with residue 1, we had found that Riemann zeta function depended intimately on properties of gamma function, which was a new gate for solving complex problems related to zeta function.