On the elegance of Ramanujan's series for $\pi$
Number Theory
2021-04-27 v1
Abstract
Re presenting the traditional proof of Srinivasa Ramanujan's own favorite series for the reciprocal of :\begin{equation}\frac{1}{\pi} = \frac{\sqrt{8}}{9801} \sum_{n=0}^{+\infty} \frac{(4n)!}{(n!)^4} \frac{1103 + 26390n}{396^{4n}} \; \text{,}\end{equation}as well as several other examples of Ramanujan's infinite series. As a matter of fact, the derivation of such formulae has involved specialized knowledge of identities of classical functions and modular functions.
Cite
@article{arxiv.2104.12412,
title = {On the elegance of Ramanujan's series for $\pi$},
author = {Chieh-Lei Wong},
journal= {arXiv preprint arXiv:2104.12412},
year = {2021}
}