The fastest series for $1/\pi$ due to Ramanujan. Proofs from modular polynomials

Abstract

First we give general formulas for proving real or complex Ramanujan series for $1/\pi$. Then, as an example, we apply them for providing complete proofs of the fastest series for $1/\pi$ due to Ramanujan using Russell and Weber modular polynomials. We recommend the reader to use a Maple program which is in the web of the author for automatically proving any Ramanujan-type series for $1/\pi$.