{"id":"https://openalex.org/W2018928782","doi":"https://doi.org/10.1090/s0025-5718-2014-02768-3","title":"Computation and theory of extended Mordell-Tornheim-Witten sums","display_name":"Computation and theory of extended Mordell-Tornheim-Witten sums","publication_year":2014,"publication_date":"2014-01-23","ids":{"openalex":"https://openalex.org/W2018928782","doi":"https://doi.org/10.1090/s0025-5718-2014-02768-3","mag":"2018928782"},"language":"en","primary_location":{"id":"doi:10.1090/s0025-5718-2014-02768-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02768-3","pdf_url":"https://www.ams.org/mcom/2014-83-288/S0025-5718-2014-02768-3/S0025-5718-2014-02768-3.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":null,"license_id":null,"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":"bronze","oa_url":"https://www.ams.org/mcom/2014-83-288/S0025-5718-2014-02768-3/S0025-5718-2014-02768-3.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5081580336","display_name":"David H. Bailey","orcid":"https://orcid.org/0000-0002-7574-8342"},"institutions":[{"id":"https://openalex.org/I148283060","display_name":"Lawrence Berkeley National Laboratory","ror":"https://ror.org/02jbv0t02","country_code":"US","type":"facility","lineage":["https://openalex.org/I1330989302","https://openalex.org/I148283060","https://openalex.org/I39565521"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"David Bailey","raw_affiliation_strings":["Lawrence Berkeley National Laboratory, Berkeley, California 94720","#N#\u00a7Lawrence Berkeley National Laboratory, Berkeley, California 94720"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Lawrence Berkeley National Laboratory, Berkeley, California 94720","institution_ids":["https://openalex.org/I148283060"]},{"raw_affiliation_string":"#N#\u00a7Lawrence Berkeley National Laboratory, Berkeley, California 94720","institution_ids":["https://openalex.org/I148283060"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5088720034","display_name":"Jonathan M. Borwein","orcid":"https://orcid.org/0000-0002-1263-0646"},"institutions":[{"id":"https://openalex.org/I78757542","display_name":"University of Newcastle Australia","ror":"https://ror.org/00eae9z71","country_code":"AU","type":"education","lineage":["https://openalex.org/I78757542"]}],"countries":["AU"],"is_corresponding":false,"raw_author_name":"Jonathan Borwein","raw_affiliation_strings":["CARMA, University of Newcastle, Callaghan, NSW 2308, Australia and Distinguished Professor King Abdulaziz University, Jeddah"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CARMA, University of Newcastle, Callaghan, NSW 2308, Australia and Distinguished Professor King Abdulaziz University, Jeddah","institution_ids":["https://openalex.org/I78757542"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5111508743","display_name":"Richard E. Crandall","orcid":null},"institutions":[{"id":"https://openalex.org/I55486353","display_name":"Reed College","ror":"https://ror.org/00a6ram87","country_code":"US","type":"education","lineage":["https://openalex.org/I55486353"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Richard Crandall","raw_affiliation_strings":["Center for Advanced Computation, Reed College, Portland, Oregon 97202"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Advanced Computation, Reed College, Portland, Oregon 97202","institution_ids":["https://openalex.org/I55486353"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":8.4153,"has_fulltext":true,"cited_by_count":27,"citation_normalized_percentile":{"value":0.98492889,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":88,"max":99},"biblio":{"volume":"83","issue":"288","first_page":"1795","last_page":"1821"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":1.0,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/T11166","display_name":"Analytic Number Theory Research","score":0.9988999962806702,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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":0.8318488597869873},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.7395732402801514},{"id":"https://openalex.org/keywords/eulerian-path","display_name":"Eulerian path","score":0.6093475818634033},{"id":"https://openalex.org/keywords/numerical-integration","display_name":"Numerical integration","score":0.5978541374206543},{"id":"https://openalex.org/keywords/explicit-formulae","display_name":"Explicit formulae","score":0.5204613208770752},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5166402459144592},{"id":"https://openalex.org/keywords/integration-by-parts","display_name":"Integration by parts","score":0.5085688829421997},{"id":"https://openalex.org/keywords/riemann-zeta-function","display_name":"Riemann zeta function","score":0.49122923612594604},{"id":"https://openalex.org/keywords/symbolic-computation","display_name":"Symbolic computation","score":0.4833078384399414},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.48009732365608215},{"id":"https://openalex.org/keywords/order-of-integration","display_name":"Order of integration (calculus)","score":0.4567774832248688},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4447774291038513},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.38666483759880066},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3709993064403534},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.25369179248809814},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.15622478723526}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8318488597869873},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.7395732402801514},{"id":"https://openalex.org/C43058520","wikidata":"https://www.wikidata.org/wiki/Q624580","display_name":"Eulerian path","level":3,"score":0.6093475818634033},{"id":"https://openalex.org/C127349201","wikidata":"https://www.wikidata.org/wiki/Q753445","display_name":"Numerical integration","level":2,"score":0.5978541374206543},{"id":"https://openalex.org/C27783845","wikidata":"https://www.wikidata.org/wiki/Q5421272","display_name":"Explicit formulae","level":2,"score":0.5204613208770752},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5166402459144592},{"id":"https://openalex.org/C118365987","wikidata":"https://www.wikidata.org/wiki/Q273328","display_name":"Integration by parts","level":2,"score":0.5085688829421997},{"id":"https://openalex.org/C35235930","wikidata":"https://www.wikidata.org/wiki/Q187235","display_name":"Riemann zeta function","level":2,"score":0.49122923612594604},{"id":"https://openalex.org/C110812573","wikidata":"https://www.wikidata.org/wiki/Q175515","display_name":"Symbolic computation","level":2,"score":0.4833078384399414},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.48009732365608215},{"id":"https://openalex.org/C38582570","wikidata":"https://www.wikidata.org/wiki/Q3825182","display_name":"Order of integration (calculus)","level":2,"score":0.4567774832248688},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4447774291038513},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.38666483759880066},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3709993064403534},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.25369179248809814},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.15622478723526},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C53469067","wikidata":"https://www.wikidata.org/wiki/Q505735","display_name":"Lagrangian","level":2,"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/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"doi:10.1090/s0025-5718-2014-02768-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02768-3","pdf_url":"https://www.ams.org/mcom/2014-83-288/S0025-5718-2014-02768-3/S0025-5718-2014-02768-3.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":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Mathematics of Computation","raw_type":"journal-article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.303.9501","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.303.9501","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://carmasite.newcastle.edu.au/jon/MTW1.pdf","raw_type":"text"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.800.89","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.800.89","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.davidhbailey.com/dhbpapers/BBC.pdf","raw_type":"text"},{"id":"pmh:oai:figshare.com:article/28958570","is_oa":true,"landing_page_url":"https://figshare.com/articles/journal_contribution/Computation_and_theory_of_extended_Mordell-Tornheim-Witten_sums/28958570","pdf_url":null,"source":{"id":"https://openalex.org/S4377196282","display_name":"Figshare","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210132348","host_organization_name":"Figshare (United Kingdom)","host_organization_lineage":["https://openalex.org/I4210132348"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Text"},{"id":"pmh:uon:14096","is_oa":false,"landing_page_url":"http://hdl.handle.net/1959.13/1042663","pdf_url":null,"source":{"id":"https://openalex.org/S4377196471","display_name":"NOVA (University of Newcastle Australia)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I78757542","host_organization_name":"University of Newcastle Australia","host_organization_lineage":["https://openalex.org/I78757542"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"journal article"}],"best_oa_location":{"id":"doi:10.1090/s0025-5718-2014-02768-3","is_oa":true,"landing_page_url":"https://doi.org/10.1090/s0025-5718-2014-02768-3","pdf_url":"https://www.ams.org/mcom/2014-83-288/S0025-5718-2014-02768-3/S0025-5718-2014-02768-3.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":null,"license_id":null,"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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2018928782.pdf","grobid_xml":"https://content.openalex.org/works/W2018928782.grobid-xml"},"referenced_works_count":42,"referenced_works":["https://openalex.org/W17196750","https://openalex.org/W167554446","https://openalex.org/W326327467","https://openalex.org/W1483793120","https://openalex.org/W1527616100","https://openalex.org/W1563216928","https://openalex.org/W1827962746","https://openalex.org/W1861266970","https://openalex.org/W1871270088","https://openalex.org/W1966291353","https://openalex.org/W1995253002","https://openalex.org/W2001083095","https://openalex.org/W2002107775","https://openalex.org/W2011295993","https://openalex.org/W2019045525","https://openalex.org/W2034274942","https://openalex.org/W2040728844","https://openalex.org/W2057233765","https://openalex.org/W2060139352","https://openalex.org/W2095709299","https://openalex.org/W2098046865","https://openalex.org/W2102562169","https://openalex.org/W2102591969","https://openalex.org/W2121848241","https://openalex.org/W2137946669","https://openalex.org/W2141060935","https://openalex.org/W2142767202","https://openalex.org/W2161056331","https://openalex.org/W2170573174","https://openalex.org/W2225503362","https://openalex.org/W2300811405","https://openalex.org/W2330070957","https://openalex.org/W2480836127","https://openalex.org/W2495205774","https://openalex.org/W2739367777","https://openalex.org/W2797005790","https://openalex.org/W2964005897","https://openalex.org/W4242849907","https://openalex.org/W4252792996","https://openalex.org/W4285719527","https://openalex.org/W6606883824","https://openalex.org/W6611378559"],"related_works":["https://openalex.org/W2773153763","https://openalex.org/W2996016345","https://openalex.org/W4288019650","https://openalex.org/W3185914399","https://openalex.org/W2964201476","https://openalex.org/W4297737575","https://openalex.org/W4389325459","https://openalex.org/W2096017817","https://openalex.org/W2050208332","https://openalex.org/W2035865380"],"abstract_inverted_index":{"We":[0,53,67],"consider":[1],"some":[2,34],"fundamental":[3],"generalized":[4],"Mordell\u2013Tornheim\u2013Witten":[5],"(MTW)":[6],"zeta-function":[7],"values":[8,18],"along":[9],"with":[10,16,96],"their":[11,94],"derivatives,":[12],"and":[13,33,37,93],"explore":[14],"connections":[15],"multiple-zeta":[17],"(MZVs).":[19],"To":[20],"achieve":[21],"this,":[22],"we":[23,83],"make":[24],"use":[25],"of":[26,63,74,91],"symbolic":[27],"integration,":[28,32],"high":[29],"precision":[30],"numerical":[31,89],"interesting":[35],"combinatorics":[36],"special-function":[38],"theory.":[39],"Our":[40],"original":[41],"motivation":[42],"was":[43],"to":[44,56,98],"represent":[45],"unresolved":[46],"constructs":[47],"such":[48,59],"as":[49],"Eulerian":[50],"log-gamma":[51],"integrals.":[52],"are":[54],"able":[55],"resolve":[57],"all":[58],"integrals":[60],"in":[61],"terms":[62],"an":[64],"MTW":[65,75],"basis.":[66],"also":[68],"present,":[69],"for":[70,87],"a":[71],"substantial":[72],"subset":[73],"values,":[76],"explicit":[77],"closed-form":[78],"expressions.":[79],"In":[80],"the":[81],"process,":[82],"significantly":[84],"extend":[85],"methods":[86],"high-precision":[88],"computation":[90],"polylogarithms":[92],"derivatives":[95],"respect":[97],"order.":[99]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":4},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":1},{"year":2017,"cited_by_count":5},{"year":2016,"cited_by_count":6},{"year":2015,"cited_by_count":3},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-08-27T14:10:00.468798","created_date":"2025-10-10T00:00:00"}