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 d decimal digits have time complexity O(M(d) log2d) and space complexity of O(d log d) or O(d). 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).