Computing hypergeometric functions rigorously
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| dc.contributor.author | JOHANSSON, Fredrik | |
| dc.date.accessioned | 2024-04-04T03:14:26Z | |
| dc.date.available | 2024-04-04T03:14:26Z | |
| dc.date.issued | 2019-08-08 | |
| dc.identifier.issn | 0098-3500 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194056 | |
| dc.description.abstractEn | We present an efficient implementation of hypergeometric functions in arbitrary-precision interval arithmetic. The functions 0F1, 1F1, 2F1 and 2F0 (or the Kummer U-function) are supported for unrestricted complex parameters and argument, and by extension, we cover exponential and trigonometric integrals, error functions, Fresnel integrals, incomplete gamma and beta functions, Bessel functions, Airy functions, Legendre functions, Jacobi polynomials, complete elliptic integrals, and other special functions. The output can be used directly for interval computations or to generate provably correct floating-point approximations in any format. Performance is competitive with earlier arbitrary-precision software, and sometimes orders of magnitude faster. We also partially cover the generalized hypergeometric function pFq and computation of high-order parameter derivatives. | |
| dc.language.iso | en | |
| dc.publisher | Association for Computing Machinery | |
| dc.rights.uri | http://creativecommons.org/licenses/by/ | |
| dc.subject.en | orthogonal polynomials | |
| dc.subject.en | Bessel functions | |
| dc.subject.en | arbitrary-precision arithmetic | |
| dc.subject.en | hypergeometric functions | |
| dc.subject.en | interval arithmetic | |
| dc.subject.en | automatic differentiation | |
| dc.title.en | Computing hypergeometric functions rigorously | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1145/3328732 | |
| dc.subject.hal | Informatique [cs]/Logiciel mathématique [cs.MS] | |
| dc.subject.hal | Informatique [cs]/Analyse numérique [cs.NA] | |
| dc.subject.hal | Informatique [cs]/Calcul formel [cs.SC] | |
| dc.description.sponsorshipEurope | Algorithmic Number Theory in Computer Science | |
| bordeaux.journal | ACM Transactions on Mathematical Software | |
| bordeaux.page | 1-26 | |
| bordeaux.volume | 45 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 3 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01336266 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01336266v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=ACM%20Transactions%20on%20Mathematical%20Software&rft.date=2019-08-08&rft.volume=45&rft.issue=3&rft.spage=1-26&rft.epage=1-26&rft.eissn=0098-3500&rft.issn=0098-3500&rft.au=JOHANSSON,%20Fredrik&rft.genre=article |
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