On the elegance of Ramanujan's series for $\pi$.
Résumé
Re presenting the traditional proof of Srinivasa Ramanujan's own favorite series for the reciprocal of $\pi$ :
\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.
Origine : Fichiers produits par l'(les) auteur(s)