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

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 Apéry-like irrationality proof could be found for this constant.

Improved version of the previous manuscript, with revised text and small corrections. 11 pages, 1 table. Submitted (06/03/2017)

References in corpus (3)

• Open Conjectures on Congruences
• An Euler-type formula for $\beta (2n)$ and closed-form expressions for a class of zeta series
• Some conjectures on congruences

Cited by in corpus (1)

• Irrationality of the Zeta Constants