{"id":"https://openalex.org/W2068728923","doi":"https://doi.org/10.1007/bf02124750","title":"On the LambertW function","display_name":"On the LambertW function","publication_year":1996,"publication_date":"1996-12-01","ids":{"openalex":"https://openalex.org/W2068728923","doi":"https://doi.org/10.1007/bf02124750","mag":"2068728923"},"language":"en","primary_location":{"id":"doi:10.1007/bf02124750","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02124750","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5044605948","display_name":"Robert M. Corless","orcid":"https://orcid.org/0000-0003-0515-1572"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":true,"raw_author_name":"R. M. Corless","raw_affiliation_strings":["Department of Applied Mathematics, University of Western Ontario London, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Western Ontario London, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013025384","display_name":"Gast\u00f3n H. Gonnet","orcid":null},"institutions":[{"id":"https://openalex.org/I35440088","display_name":"ETH Zurich","ror":"https://ror.org/05a28rw58","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I35440088"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"G. H. Gonnet","raw_affiliation_strings":["Institut f\u00fcr Wissenschaftliches Rechnen ETH, Z\u00fcrich, Switzerland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institut f\u00fcr Wissenschaftliches Rechnen ETH, Z\u00fcrich, Switzerland","institution_ids":["https://openalex.org/I35440088"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081424980","display_name":"D. E. G. Hare","orcid":null},"institutions":[{"id":"https://openalex.org/I151746483","display_name":"University of Waterloo","ror":"https://ror.org/01aff2v68","country_code":"CA","type":"education","lineage":["https://openalex.org/I151746483"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"D. E. G. Hare","raw_affiliation_strings":["Symbolic Computation Group, University of Waterloo, Waterloo, Canada#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Symbolic Computation Group, University of Waterloo, Waterloo, Canada#TAB#","institution_ids":["https://openalex.org/I151746483"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051667032","display_name":"David J. Jeffrey","orcid":"https://orcid.org/0000-0002-2161-6803"},"institutions":[{"id":"https://openalex.org/I125749732","display_name":"Western University","ror":"https://ror.org/02grkyz14","country_code":"CA","type":"education","lineage":["https://openalex.org/I125749732"]}],"countries":["CA"],"is_corresponding":false,"raw_author_name":"D. J. Jeffrey","raw_affiliation_strings":["Department of Applied Mathematics, University of Western Ontario London, Canada"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, University of Western Ontario London, Canada","institution_ids":["https://openalex.org/I125749732"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5110826490","display_name":"Donald E. Knuth","orcid":null},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"D. E. Knuth","raw_affiliation_strings":["Department of Computer Science , Stanford University, Stanford, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Computer Science , Stanford University, Stanford, USA","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5044605948"],"corresponding_institution_ids":["https://openalex.org/I125749732"],"apc_list":{"value":2390,"currency":"EUR","value_usd":2990},"apc_paid":null,"fwci":21.8212,"has_fulltext":false,"cited_by_count":6153,"citation_normalized_percentile":{"value":0.99820631,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":99,"max":100},"biblio":{"volume":"5","issue":"1","first_page":"329","last_page":"359"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12677","display_name":"Sports Dynamics and Biomechanics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T12677","display_name":"Sports Dynamics and Biomechanics","score":0.9975000023841858,"subfield":{"id":"https://openalex.org/subfields/2204","display_name":"Biomedical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12250","display_name":"Experimental and Theoretical Physics Studies","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/computational-science-and-engineering","display_name":"Computational Science and Engineering","score":0.7211530804634094},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5247552394866943},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.507243812084198},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.24105262756347656},{"id":"https://openalex.org/keywords/biology","display_name":"Biology","score":0.11361336708068848},{"id":"https://openalex.org/keywords/evolutionary-biology","display_name":"Evolutionary biology","score":0.07167515158653259}],"concepts":[{"id":"https://openalex.org/C68597687","wikidata":"https://www.wikidata.org/wiki/Q362601","display_name":"Computational Science and Engineering","level":2,"score":0.7211530804634094},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5247552394866943},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.507243812084198},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.24105262756347656},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.11361336708068848},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.07167515158653259}],"mesh":[],"locations_count":7,"locations":[{"id":"doi:10.1007/bf02124750","is_oa":false,"landing_page_url":"https://doi.org/10.1007/bf02124750","pdf_url":null,"source":{"id":"https://openalex.org/S57050787","display_name":"Advances in Computational Mathematics","issn_l":"1019-7168","issn":["1019-7168","1572-9044"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Computational Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.112.6117","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.112.6117","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lacim.uqam.ca/~plouffe/oeis/archive_in_pdf/lambertw.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.31.5932","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.31.5932","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ftp://ftp.inria.fr/lang/maple/5.3/share/LambertW.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.33.3583","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.33.3583","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.apmaths.uwo.ca/~rcorless/frames/PAPERS/LambertW/LambertW.ps.Z","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.493.2397","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.493.2397","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.52.6346","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.52.6346","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.apmaths.uwo.ca/~djeffrey/Offprints/W-adv-cm.ps","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.86.9305","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.86.9305","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.cs.uwaterloo.ca/research/tr/1993/03/W.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320334593","display_name":"Natural Sciences and Engineering Research Council of Canada","ror":"https://ror.org/01h531d29"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":67,"referenced_works":["https://openalex.org/W102324627","https://openalex.org/W119916070","https://openalex.org/W176859057","https://openalex.org/W194256761","https://openalex.org/W589198329","https://openalex.org/W592059636","https://openalex.org/W1524707262","https://openalex.org/W1540938302","https://openalex.org/W1543220654","https://openalex.org/W1554813786","https://openalex.org/W1579306088","https://openalex.org/W1585070348","https://openalex.org/W1597251915","https://openalex.org/W1611032851","https://openalex.org/W1628745019","https://openalex.org/W1964362178","https://openalex.org/W1965853706","https://openalex.org/W1979064007","https://openalex.org/W1983072075","https://openalex.org/W1985494751","https://openalex.org/W1993744672","https://openalex.org/W1996343555","https://openalex.org/W2002164453","https://openalex.org/W2003538272","https://openalex.org/W2009767855","https://openalex.org/W2010818373","https://openalex.org/W2010894431","https://openalex.org/W2014172170","https://openalex.org/W2014562853","https://openalex.org/W2027130327","https://openalex.org/W2041109929","https://openalex.org/W2048056120","https://openalex.org/W2048858877","https://openalex.org/W2049817705","https://openalex.org/W2056515188","https://openalex.org/W2066824935","https://openalex.org/W2067473936","https://openalex.org/W2074251375","https://openalex.org/W2087979207","https://openalex.org/W2091190547","https://openalex.org/W2091323212","https://openalex.org/W2091859203","https://openalex.org/W2092866774","https://openalex.org/W2121373282","https://openalex.org/W2167266655","https://openalex.org/W2276336683","https://openalex.org/W2291540719","https://openalex.org/W2304453959","https://openalex.org/W2317414552","https://openalex.org/W2319298080","https://openalex.org/W2322918871","https://openalex.org/W2616697817","https://openalex.org/W2752954798","https://openalex.org/W2795721869","https://openalex.org/W2905613034","https://openalex.org/W3005154287","https://openalex.org/W4205333027","https://openalex.org/W4205727720","https://openalex.org/W4212799367","https://openalex.org/W4214710890","https://openalex.org/W4230140608","https://openalex.org/W4252247111","https://openalex.org/W4253027624","https://openalex.org/W4285719527","https://openalex.org/W4293087381","https://openalex.org/W6606990341","https://openalex.org/W6819924498"],"related_works":["https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W4245490552","https://openalex.org/W4225152035","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587224694","https://openalex.org/W2911598644","https://openalex.org/W2042127053"],"abstract_inverted_index":null,"counts_by_year":[{"year":2026,"cited_by_count":79},{"year":2025,"cited_by_count":287},{"year":2024,"cited_by_count":276},{"year":2023,"cited_by_count":306},{"year":2022,"cited_by_count":332},{"year":2021,"cited_by_count":357},{"year":2020,"cited_by_count":382},{"year":2019,"cited_by_count":364},{"year":2018,"cited_by_count":294},{"year":2017,"cited_by_count":332},{"year":2016,"cited_by_count":334},{"year":2015,"cited_by_count":291},{"year":2014,"cited_by_count":316},{"year":2013,"cited_by_count":282},{"year":2012,"cited_by_count":282}],"updated_date":"2026-05-20T08:49:12.498775","created_date":"2025-10-10T00:00:00"}
