Experimental Mathematics

A New Method to Obtain Series for $1 / \pi$ and $1 / \pi^2$

Jesús Guillera

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Abstract

We give several conjectures that allow us to derive many series for {\small $ 1/ \pi$} and {\small $ 1/ \pi^2$}. These series include Ramanujan's series, as well as those associated with the Domb numbers and Apéry numbers. We have checked the conjectures numerically in many examples with a precision of two hundred digits.

Article information

Source
Experiment. Math., Volume 15, Number 1 (2006), 83-89.

Dates
First available in Project Euclid: 16 June 2006

Permanent link to this document
https://projecteuclid.org/euclid.em/1150476906

Mathematical Reviews number (MathSciNet)
MR2229388

Zentralblatt MATH identifier
1113.11076

Keywords
Ramanujan series series for 1/π series for 1/π2 Domb numbers Apéry numbers

Citation

Guillera, Jesús. A New Method to Obtain Series for $1 / \pi$ and $1 / \pi^2$. Experiment. Math. 15 (2006), no. 1, 83--89. https://projecteuclid.org/euclid.em/1150476906


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