Time-and space-efficient evaluation of some hypergeometric constants

The currently best known algorithms for the numerical evaluation of hypergeometric constants such as Ç(3) to <i>d</i> decimal digits have time complexity <i>O</i>(<i>M</i>(<i>d</i>) log²<i>d</i>) and space complexity of <i>O</i>(<i>d</i> log <i>d</i>) or <i>O</i>(<i>d</i>). Following work from Cheng, Gergel, Kim and Zima, we present a new algorithm with the same asymptotic complexity, but more efficient in practice. Our implementation of this algorithm improves over existing programs for the computation of Π, and we announce a new record of 2 billion digits for Ç(3).