Understanding Ramanujan Summation

Abstract

Beginning from Euler, several summation methods were proposed by mathematicians of various times. One such curious summation method was proposed by Indian Mathematical Genius Srinivasa Ramanujan in his famous notebooks. Though the significance of those equations was well known today to most modern mathematicians, those equations could be proved using complex analysis concepts. In this paper, I present a novel method to arrive at the same equations scribbled by Ramanujan nearly a century ago, without complex variables but through basic integrals of real valued functions.