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Arbitrary-precision computation of the gamma function

Fredrik Johansson 1 
1 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
Abstract : We discuss the best methods available for computing the gamma function $\Gamma(z)$ in arbitrary-precision arithmetic with rigorous error bounds. We address different cases: rational, algebraic, real or complex arguments; large or small arguments; low or high precision; with or without precomputation. The methods also cover the log-gamma function $\log \Gamma(z)$, the digamma function $\psi(z)$, and derivatives $\Gamma^{(n)}(z)$ and $\psi^{(n)}(z)$. Besides attempting to summarize the existing state of the art, we present some new formulas, estimates, bounds and algorithmic improvements and discuss implementation results.
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Contributor : Fredrik Johansson Connect in order to contact the contributor
Submitted on : Thursday, September 16, 2021 - 2:48:26 PM
Last modification on : Wednesday, February 2, 2022 - 3:54:15 PM
Long-term archiving on: : Friday, December 17, 2021 - 7:10:42 PM


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  • HAL Id : hal-03346642, version 1
  • ARXIV : 2109.08392



Fredrik Johansson. Arbitrary-precision computation of the gamma function. 2021. ⟨hal-03346642⟩



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