Journal of Mathematics and Statistics

Proof of Bernhard Riemann's Functional Equation using Gamma Function

Mbaïtiga Zacharie

DOI : 10.3844/jmssp.2008.181.185

Journal of Mathematics and Statistics

Volume 4, Issue 3

Pages 181-185

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.

Copyright

© 2008 Mbaïtiga Zacharie. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.