# Ramanujan-type formulae for 1/pi: a second wind?

@article{Zudilin2008RamanujantypeFF, title={Ramanujan-type formulae for 1/pi: a second wind?}, author={Wadim Zudilin}, journal={arXiv: Number Theory}, year={2008}, pages={179-188} }

In 1914 S. Ramanujan recorded a list of 17 series for 1=…. We survey the methods of proofs of Ramanujan’s formulae and indicate recently discovered generalisations, some of which are not yet proven. Let us start with two signiflcant events of the 20th century, in the opposite historical order. At flrst glance, the stories might be thought of a difierent nature.

#### 44 Citations

A method for proving Ramanujan’s series for $$1/\pi $$1/π

- Mathematics
- The Ramanujan Journal
- 2019

In a famous paper of 1914 Ramanujan gave a list of 17 extraordinary formulas for the number $$1/\pi $$1/π. In this paper we explain a general method to prove them, based on some ideas of James Wan… Expand

Rational analogues of Ramanujan's series for 1/π†

- Mathematics
- Mathematical Proceedings of the Cambridge Philosophical Society
- 2012

Abstract A general theorem is stated that unifies 93 rational Ramanujan-type series for 1/π, 40 of which are believed to be new. Moreover, each series is shown to have a companion identity, thereby… Expand

Divergent Ramanujan-type supercongruences

- Mathematics
- 2012

"Divergent" Ramanujan-type series for $1/\pi$ and $1/\pi^2$ provide us with new nice examples of supercongruences of the same kind as those related to the convergent cases. In this paper we manage to… Expand

Kind of proofs of Ramanujan-like series

- Mathematics
- 2012

We make a summary of the different types of proofs adding some new ideas. In addition we conjecture some relations which could be necessary in "modular type proofs" (not still found) of the… Expand

Mosaic Supercongruences of Ramanujan Type

- Computer Science, Mathematics
- Exp. Math.
- 2012

Congruences of supercongruences of Ramanujan type observed by L. Van Hamme and W. Zudilin are presented, inspired by Ramanuja-type series that involve quadratic algebraic numbers. Expand

A new Ramanujan-like series for $1/\pi^2$

- Mathematics
- 2010

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

Ramanujan-type supercongruences

- Mathematics
- 2009

Abstract We present several supercongruences that may be viewed as p-adic analogues of Ramanujan-type series for 1 / π and 1 / π 2 , and prove three of these examples.

On the (K.2) supercongruence of Van Hamme

- Mathematics
- 2016

Abstract We prove the last remaining case of the original 13 Ramanujan-type supercongruence conjectures due to Van Hamme from 1997. The proof utilizes classical congruences and a WZ pair due to… Expand

Lost in translation

- Mathematics
- 2012

The principal goal of this note is to set some grounds about applicability of algebraic transformations of (arithmetic) hypergeometric series for proving Ramanujan’s formulae for 1/π and their… Expand

Sporadic sequences, modular forms and new series for 1/π

- Mathematics
- 2012

Two new sequences, which are analogues of six sporadic examples of D. Zagier, are presented. The connection with modular forms is established and some new series for 1/π are deduced. The experimental… Expand

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