# Time- and Space-Efficient Evaluation of Some Hypergeometric Constants

2 CACAO - Curves, Algebra, Computer Arithmetic, and so On
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
Abstract : 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 $\zeta(3)$.
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Reports

Cited literature [17 references]

https://hal.inria.fr/inria-00126428
Contributor : Rapport de Recherche Inria <>
Submitted on : Thursday, January 25, 2007 - 2:24:04 PM
Last modification on : Friday, June 28, 2019 - 2:42:04 PM
Long-term archiving on : Tuesday, September 21, 2010 - 11:52:39 AM

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### Citation

Howard Cheng, Guillaume Hanrot, Emmanuel Thomé, Eugene Zima, Paul Zimmermann. Time- and Space-Efficient Evaluation of Some Hypergeometric Constants. [Research Report] RR-6105, INRIA. 2007. ⟨inria-00126428v2⟩

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