A method for proving Ramanujan series for $1/\pi$

TL;DR

This paper introduces a general method to prove Ramanujan's formulas for 1/π, combining Wan's original idea with new approaches, advancing the understanding of these remarkable series.

Contribution

It presents a novel, unified method for proving Ramanujan's π-series, expanding on Wan's idea and offering a systematic approach.

Findings

Successfully proves multiple Ramanujan series for 1/π

Provides a new framework for understanding Ramanujan's formulas

Enhances mathematical tools for series proofs

Abstract

In a famous paper of $1914$ Ramanujan gave a list of $17$ extraordinary formulas for the number $\pi$. In this paper we explain a general method to prove them, based on an original idea of James Wan and in some own ideas.