JOHANSSON, Fredrik

doi:10.5206/mt.v3i1.14591

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Licencia de uso del documento

JOHANSSON, Fredrik
Lithe and fast algorithmic number theory [LFANT]
Analyse cryptographique et arithmétique [CANARI]

Idioma

Article de revue

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Maple Transactions. 2023-02-01, vol. 3, n° 1

Western Libraries Western University

Resumen en inglés

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.< Leer menos

URI

https://oskar-bordeaux.fr/handle/20.500.12278/191483

DOI

http://dx.doi.org/10.5206/mt.v3i1.14591

Proyecto ANR

Sûreté numérique pour les preuves assistées par ordinateur - ANR-20-CE48-0014

Orígen

Importado de Hal

Centros de investigación

Institut de Mathématiques de Bordeaux (IMB) - UMR 5251