Arbitrary-precision computation of the gamma function
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Analyse cryptographique et arithmétique [CANARI] | |
| dc.contributor.author | JOHANSSON, Fredrik | |
| dc.date.accessioned | 2024-04-04T02:45:37Z | |
| dc.date.available | 2024-04-04T02:45:37Z | |
| dc.date.issued | 2023-02-01 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191483 | |
| dc.description.abstractEn | 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. | |
| dc.description.sponsorship | Sûreté numérique pour les preuves assistées par ordinateur - ANR-20-CE48-0014 | |
| dc.language.iso | en | |
| dc.publisher | Western Libraries Western University | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.title.en | Arbitrary-precision computation of the gamma function | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.5206/mt.v3i1.14591 | |
| dc.subject.hal | Informatique [cs]/Analyse numérique [cs.NA] | |
| dc.subject.hal | Informatique [cs]/Logiciel mathématique [cs.MS] | |
| dc.subject.hal | Mathématiques [math]/Analyse classique [math.CA] | |
| dc.identifier.arxiv | 2109.08392 | |
| bordeaux.journal | Maple Transactions | |
| bordeaux.volume | 3 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-03346642 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03346642v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Maple%20Transactions&rft.date=2023-02-01&rft.volume=3&rft.issue=1&rft.au=JOHANSSON,%20Fredrik&rft.genre=article |
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