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arXiv · 1207.3139

A rapidly converging Ramanujan-type series for Catalan's constant

F. M. S. Lima
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Abstract

In this note, by making use of a known hypergeometric series identity, I prove two Ramanujan-type series for the Catalan's constant. The convergence rate of these central binomial series surpasses those of all known similar series, including a classical formula by Ramanujan and a recent formula by Lupas. Interestingly, this suggests that an Ap\'{e}ry-like irrationality proof could be found for this constant.

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F. M. S. Lima. 2012-07-13. A rapidly converging Ramanujan-type series for Catalan's constant. https://arxiv.org/abs/1207.3139

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