The Zeta Function Derivation of the Ramanujan’s Summation
Please note that the famous Ramanujan Summation has three derivations: Heuristic (Infinity Manipulation), Zeta Function Regularisation and the Cutoff Regularisation. This article presents represents the Zeta Function Regularisation proof of the summation. To read more on the other methods of summation, click on this . Moving on to the article: In one of my previous articles , I talked about the Ramanujan’s summation and its derivation with countable Heuristics method, infinity manipulation. It was an interesting approach, however, the hypothesis that 1+2+3+4+5+… = -1/12 is a viable hypothesis in many perspectives. For the purpose of this article, I will be talking about the Riemann Zeta Function, a complex analysis method, and how it is used to prove the Ramanujan Summation through a different perspective. The Riemann Zeta Function is defined as follows: This function is interesting as it always converges into a fraction including a power of Pi for even integers (Bernoulli Numbers