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Arbitrary-precision computation of the gamma function

hal.structure.identifierLithe and fast algorithmic number theory [LFANT]
hal.structure.identifierAnalyse cryptographique et arithmétique [CANARI]
dc.contributor.authorJOHANSSON, Fredrik
dc.date.accessioned2024-04-04T02:45:37Z
dc.date.available2024-04-04T02:45:37Z
dc.date.issued2023-02-01
dc.identifier.urihttps://oskar-bordeaux.fr/handle/20.500.12278/191483
dc.description.abstractEnWe 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.sponsorshipSûreté numérique pour les preuves assistées par ordinateur - ANR-20-CE48-0014
dc.language.isoen
dc.publisherWestern Libraries Western University
dc.rights.urihttp://creativecommons.org/licenses/by/
dc.title.enArbitrary-precision computation of the gamma function
dc.typeArticle de revue
dc.identifier.doi10.5206/mt.v3i1.14591
dc.subject.halInformatique [cs]/Analyse numérique [cs.NA]
dc.subject.halInformatique [cs]/Logiciel mathématique [cs.MS]
dc.subject.halMathématiques [math]/Analyse classique [math.CA]
dc.identifier.arxiv2109.08392
bordeaux.journalMaple Transactions
bordeaux.volume3
bordeaux.hal.laboratoriesInstitut de Mathématiques de Bordeaux (IMB) - UMR 5251*
bordeaux.issue1
bordeaux.institutionUniversité de Bordeaux
bordeaux.institutionBordeaux INP
bordeaux.institutionCNRS
bordeaux.peerReviewedoui
hal.identifierhal-03346642
hal.version1
hal.popularnon
hal.audienceInternationale
hal.origin.linkhttps://hal.archives-ouvertes.fr//hal-03346642v1
bordeaux.COinSctx_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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