{"id":"https://openalex.org/W2002573724","doi":"https://doi.org/10.1090/s0025-5718-09-02222-4","title":"High precision computation of a constant in the theory of trigonometric series","display_name":"High precision computation of a constant in the theory of trigonometric series","publication_year":2009,"publication_date":"2009-02-09","ids":{"openalex":"https://openalex.org/W2002573724","doi":"https://doi.org/10.1090/s0025-5718-09-02222-4","mag":"2002573724"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-09-02222-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02222-4","pdf_url":"https://www.ams.org/mcom/2009-78-268/S0025-5718-09-02222-4/S0025-5718-09-02222-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://www.ams.org/mcom/2009-78-268/S0025-5718-09-02222-4/S0025-5718-09-02222-4.pdf","any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5068976921","display_name":"Juan Arias de Reyna","orcid":"https://orcid.org/0000-0003-3348-4374"},"institutions":[{"id":"https://openalex.org/I79238269","display_name":"Universidad de Sevilla","ror":"https://ror.org/03yxnpp24","country_code":"ES","type":"education","lineage":["https://openalex.org/I79238269"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"J. de Reyna","raw_affiliation_strings":["Facultad de Matem\u00c3\u00a1ticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain","Facultad de Matem\u00e1ticas, Universidad de Sevilla, Apdo.\u00a01160, 41080-Sevilla, Spain"],"affiliations":[{"raw_affiliation_string":"Facultad de Matem\u00c3\u00a1ticas, Universidad de Sevilla, Apdo. 1160, 41080-Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]},{"raw_affiliation_string":"Facultad de Matem\u00e1ticas, Universidad de Sevilla, Apdo.\u00a01160, 41080-Sevilla, Spain","institution_ids":["https://openalex.org/I79238269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5013780517","display_name":"J. Lune","orcid":null},"institutions":[{"id":"https://openalex.org/I1341640284","display_name":"Centrum Wiskunde & Informatica","ror":"https://ror.org/00x7ekv49","country_code":"NL","type":"facility","lineage":["https://openalex.org/I1341640284","https://openalex.org/I2800991832"]}],"countries":["NL"],"is_corresponding":false,"raw_author_name":"J. van de Lune","raw_affiliation_strings":["Langebuorren 49, 9074 CH Hallum, The Netherlands (formerly at CWI, Amsterdam)"],"affiliations":[{"raw_affiliation_string":"Langebuorren 49, 9074 CH Hallum, The Netherlands (formerly at CWI, Amsterdam)","institution_ids":["https://openalex.org/I1341640284"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5068976921"],"corresponding_institution_ids":["https://openalex.org/I79238269"],"apc_list":null,"apc_paid":null,"fwci":0.7141,"has_fulltext":true,"cited_by_count":3,"citation_normalized_percentile":{"value":0.69357692,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"78","issue":"268","first_page":"2187","last_page":"2191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9585999846458435,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11697","display_name":"Numerical Methods and Algorithms","score":0.9585999846458435,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9423999786376953,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.91839998960495,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8087117075920105},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.6758383512496948},{"id":"https://openalex.org/keywords/trigonometry","display_name":"Trigonometry","score":0.6658501625061035},{"id":"https://openalex.org/keywords/trigonometric-series","display_name":"Trigonometric series","score":0.6406393647193909},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.6385973691940308},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6018614172935486},{"id":"https://openalex.org/keywords/trigonometric-integral","display_name":"Trigonometric integral","score":0.550451397895813},{"id":"https://openalex.org/keywords/trigonometric-polynomial","display_name":"Trigonometric polynomial","score":0.5173324942588806},{"id":"https://openalex.org/keywords/integration-using-eulers-formula","display_name":"Integration using Euler's formula","score":0.43967875838279724},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"Trigonometric functions","score":0.4352300465106964},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4276996850967407},{"id":"https://openalex.org/keywords/bisection-method","display_name":"Bisection method","score":0.4135453999042511},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.36509251594543457},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.36120763421058655},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33919140696525574},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.12403765320777893},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.08263987302780151},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.08105507493019104}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8087117075920105},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.6758383512496948},{"id":"https://openalex.org/C29001434","wikidata":"https://www.wikidata.org/wiki/Q8084","display_name":"Trigonometry","level":2,"score":0.6658501625061035},{"id":"https://openalex.org/C120362076","wikidata":"https://www.wikidata.org/wiki/Q1149336","display_name":"Trigonometric series","level":2,"score":0.6406393647193909},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.6385973691940308},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6018614172935486},{"id":"https://openalex.org/C65692021","wikidata":"https://www.wikidata.org/wiki/Q1094282","display_name":"Trigonometric integral","level":3,"score":0.550451397895813},{"id":"https://openalex.org/C156760230","wikidata":"https://www.wikidata.org/wiki/Q1969650","display_name":"Trigonometric polynomial","level":3,"score":0.5173324942588806},{"id":"https://openalex.org/C65454745","wikidata":"https://www.wikidata.org/wiki/Q6043250","display_name":"Integration using Euler's formula","level":5,"score":0.43967875838279724},{"id":"https://openalex.org/C178009071","wikidata":"https://www.wikidata.org/wiki/Q93344","display_name":"Trigonometric functions","level":2,"score":0.4352300465106964},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4276996850967407},{"id":"https://openalex.org/C157544257","wikidata":"https://www.wikidata.org/wiki/Q866300","display_name":"Bisection method","level":2,"score":0.4135453999042511},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.36509251594543457},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.36120763421058655},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33919140696525574},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.12403765320777893},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.08263987302780151},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.08105507493019104},{"id":"https://openalex.org/C49608258","wikidata":"https://www.wikidata.org/wiki/Q611705","display_name":"Bicubic interpolation","level":4,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C171836373","wikidata":"https://www.wikidata.org/wiki/Q2266329","display_name":"Linear interpolation","level":3,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1090/s0025-5718-09-02222-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02222-4","pdf_url":"https://www.ams.org/mcom/2009-78-268/S0025-5718-09-02222-4/S0025-5718-09-02222-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-09-02222-4","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-09-02222-4","pdf_url":"https://www.ams.org/mcom/2009-78-268/S0025-5718-09-02222-4/S0025-5718-09-02222-4.pdf","source":{"id":"https://openalex.org/S102439543","display_name":"Mathematics of Computation","issn_l":"0025-5718","issn":["0025-5718","1088-6842"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315719","host_organization_name":"American Mathematical Society","host_organization_lineage":["https://openalex.org/P4310315719"],"host_organization_lineage_names":["American Mathematical Society"],"type":"journal"},"license":"public-domain","license_id":"https://openalex.org/licenses/public-domain","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2002573724.pdf","grobid_xml":"https://content.openalex.org/works/W2002573724.grobid-xml"},"referenced_works_count":14,"referenced_works":["https://openalex.org/W1506933769","https://openalex.org/W1972852652","https://openalex.org/W2005570059","https://openalex.org/W2019925222","https://openalex.org/W2026677102","https://openalex.org/W2067437083","https://openalex.org/W2076563420","https://openalex.org/W2085424551","https://openalex.org/W2092453786","https://openalex.org/W2120980520","https://openalex.org/W2330548796","https://openalex.org/W4230111467","https://openalex.org/W4234773450","https://openalex.org/W4240308190"],"related_works":["https://openalex.org/W657485438","https://openalex.org/W1975656026","https://openalex.org/W3205327584","https://openalex.org/W3137248282","https://openalex.org/W1846017141","https://openalex.org/W2010970866","https://openalex.org/W2081581931","https://openalex.org/W2342500772","https://openalex.org/W1998267790","https://openalex.org/W3195186546"],"abstract_inverted_index":{"Using":[0],"the":[1,6,14,20],"bisection":[2],"as":[3,5],"well":[4],"Newton-Raphson":[7],"method,":[8],"we":[9],"compute":[10],"to":[11],"high":[12],"precision":[13],"Littlewood-Salem-Izumi":[15],"constant":[16],"frequently":[17],"occurring":[18],"in":[19],"theory":[21],"of":[22],"trigonometric":[23],"sums.":[24]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2012,"cited_by_count":2}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}
