A WZ proof of Ramanujan's Formula for Pi

The known WZ-proofs for Ramanujan-type series related to $1/\pi$ gave us the insight to develop a new proof strategy based on the WZ-method. Using this approach we are able to find more generalizations and discover first WZ-proofs for certain series of this type.

Several terminating generalizations of Ramanujan's formula for $\frac{1}{\pi}$ with complete WZ proofs are given.

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.

We provide a complete proof of an impressive series for $1/\pi$ due to Ramanujan. The computations are made using MAPLE (a symbolic software).

We show with some examples how to prove some Ramanujan-type series for $1/\pi$ in an elementary way by using terminating identities.

In 1914 S. Ramanujan recorded a list of 17 series for $1/\pi$. We survey the methods of proofs of Ramanujan's formulae and indicate recently discovered generalizations, some of which are not yet proven.

Our main results are a WZ-proof of a new Ramanujan-like series for $1/\pi^2$ and a hypergeometric identity involving three series.

In this paper we want to prove some formulas listed by S. Ramanujan in his paper "Modular equations and approximations to $\pi$" \cite{24} with an elementary method.

We prove some "divergent" Ramanujan-type series for $1/\pi$ and $1/\pi^2$ applying a Barnes-integrals strategy of the WZ-method.

A family of original formulae for computing number PI and its proof are presented. An algorithm is proposed to validate the results of this new algorithm.