A rapidly converging Ramanujan-type series for Catalan's constant
Number Theory
2017-06-06 v2
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.
Keywords
Cite
@article{arxiv.1207.3139,
title = {A rapidly converging Ramanujan-type series for Catalan's constant},
author = {F. M. S. Lima},
journal= {arXiv preprint arXiv:1207.3139},
year = {2017}
}
Comments
Improved version of the previous manuscript, with revised text and small corrections. 11 pages, 1 table. Submitted (06/03/2017)