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Remembering Ramanujan

2020; Elsevier BV; Linguagem: Inglês

10.37418/amsj.9.1.38

1857-8438

R. Sivaraman,

Advanced Mathematical Identities

Mathematicians like Guido Grandi, Ernesto Cesaro and others found novel way of assigning finite sum to divergent series. This created a new scope of understanding leading to analytic continuation of real valued functions. One among such methods was called ``Ramanujan Summation'' proposed by Indian Mathematician Srinivasa Ramanujan. In this paper, I try to highlight how Ramanujan could have possibly arrived at those values by looking through his notebook jottings and extending further to provide Geometrical meaning behind those values obtained by him. Finally, I provide a novel way to arrive at the general formula obtained by Ramanujan regarding his summation of zeta function.