Time- and Space-Efficient Evaluation of Some Hypergeometric Constants
<|reference_start|>Time- and Space-Efficient Evaluation of Some Hypergeometric Constants: The currently best known algorithms for the numerical evaluation of hypergeometric constants such as $\zeta(3)$ to $d$ decimal digits have time complexity $O(M(d) \log^2 d)$ 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 slightly over existing programs for the computation of $\pi$, and we announce a new record of 2 billion digits for $\zeta(3)$.<|reference_end|>
@article{cheng2007time-,
    title={Time- and Space-Efficient Evaluation of Some Hypergeometric Constants},
    author={Howard Cheng, Guillaume Hanrot (INRIA Lorraine - LORIA), Emmanuel
  Thom'e (INRIA Lorraine - LORIA), Eugene Zima, Paul Zimmermann (INRIA
  Lorraine - LORIA)},
    journal={arXiv preprint arXiv:cs/0701151},
    year={2007},
    archivePrefix={arXiv},
    eprint={cs/0701151},
    primaryClass={cs.SC}
}