{"id":"https://openalex.org/W4306403495","doi":"https://doi.org/10.3390/axioms11100562","title":"A New First Order Expansion Formula with a Reduced Remainder","display_name":"A New First Order Expansion Formula with a Reduced Remainder","publication_year":2022,"publication_date":"2022-10-17","ids":{"openalex":"https://openalex.org/W4306403495","doi":"https://doi.org/10.3390/axioms11100562"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11100562","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100562","pdf_url":"https://www.mdpi.com/2075-1680/11/10/562/pdf?version=1666594618","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/11/10/562/pdf?version=1666594618","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003172935","display_name":"Jo\u00ebl Chaskalovic","orcid":"https://orcid.org/0000-0003-1263-5313"},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210133716","display_name":"Institut Jean Le Rond d'Alembert","ror":"https://ror.org/043we9s22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210095849","https://openalex.org/I4210133716"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Joel Chaskalovic","raw_affiliation_strings":["Jean Le Rond d\u2019Alembert, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France","Jean Le Rond d'Alembert, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France"],"raw_orcid":"https://orcid.org/0000-0003-1263-5313","affiliations":[{"raw_affiliation_string":"Jean Le Rond d\u2019Alembert, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France","institution_ids":["https://openalex.org/I4210133716","https://openalex.org/I39804081"]},{"raw_affiliation_string":"Jean Le Rond d'Alembert, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210133716"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5010654617","display_name":"Hessam Jamshidipour","orcid":null},"institutions":[{"id":"https://openalex.org/I39804081","display_name":"Sorbonne Universit\u00e9","ror":"https://ror.org/02en5vm52","country_code":"FR","type":"education","lineage":["https://openalex.org/I39804081"]},{"id":"https://openalex.org/I4210133716","display_name":"Institut Jean Le Rond d'Alembert","ror":"https://ror.org/043we9s22","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I39804081","https://openalex.org/I4210095849","https://openalex.org/I4210133716"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Hessam Jamshidipour","raw_affiliation_strings":["Jean Le Rond d\u2019Alembert, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France","Jean Le Rond d'Alembert, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Jean Le Rond d\u2019Alembert, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France","institution_ids":["https://openalex.org/I4210133716","https://openalex.org/I39804081"]},{"raw_affiliation_string":"Jean Le Rond d'Alembert, Sorbonne University, 4 Place Jussieu, CEDEX 05, 75252 Paris, France","institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210133716"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5003172935"],"corresponding_institution_ids":["https://openalex.org/I39804081","https://openalex.org/I4210133716"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.6012,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.80548751,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":99},"biblio":{"volume":"11","issue":"10","first_page":"562","last_page":"562"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9983000159263611,"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"}},"topics":[{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9983000159263611,"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/T11205","display_name":"Numerical methods in inverse problems","score":0.9980000257492065,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T10514","display_name":"Numerical methods in engineering","score":0.9976999759674072,"subfield":{"id":"https://openalex.org/subfields/2211","display_name":"Mechanics of Materials"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/remainder","display_name":"Remainder","score":0.9773577451705933},{"id":"https://openalex.org/keywords/taylor-series","display_name":"Taylor series","score":0.8563787341117859},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7425936460494995},{"id":"https://openalex.org/keywords/taylors-theorem","display_name":"Taylor's theorem","score":0.686601996421814},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.5658690929412842},{"id":"https://openalex.org/keywords/quadrature","display_name":"Quadrature (astronomy)","score":0.5425283908843994},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.5297713279724121},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5048690438270569},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4349689185619354},{"id":"https://openalex.org/keywords/divided-differences","display_name":"Divided differences","score":0.4344456195831299},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.33809590339660645},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.1318650245666504},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.09552925825119019}],"concepts":[{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.9773577451705933},{"id":"https://openalex.org/C158946198","wikidata":"https://www.wikidata.org/wiki/Q131187","display_name":"Taylor series","level":2,"score":0.8563787341117859},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7425936460494995},{"id":"https://openalex.org/C192523876","wikidata":"https://www.wikidata.org/wiki/Q1137206","display_name":"Taylor's theorem","level":3,"score":0.686601996421814},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.5658690929412842},{"id":"https://openalex.org/C62869609","wikidata":"https://www.wikidata.org/wiki/Q28137","display_name":"Quadrature (astronomy)","level":2,"score":0.5425283908843994},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.5297713279724121},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5048690438270569},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4349689185619354},{"id":"https://openalex.org/C183554904","wikidata":"https://www.wikidata.org/wiki/Q2993265","display_name":"Divided differences","level":2,"score":0.4344456195831299},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.33809590339660645},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.1318650245666504},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.09552925825119019},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","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/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C121684516","wikidata":"https://www.wikidata.org/wiki/Q7600677","display_name":"Computer graphics (images)","level":1,"score":0.0},{"id":"https://openalex.org/C502989409","wikidata":"https://www.wikidata.org/wiki/Q11425","display_name":"Animation","level":2,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"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":3,"locations":[{"id":"doi:10.3390/axioms11100562","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100562","pdf_url":"https://www.mdpi.com/2075-1680/11/10/562/pdf?version=1666594618","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:b03a7dcbfc8d4830846df676a1dcafb7","is_oa":true,"landing_page_url":"https://doaj.org/article/b03a7dcbfc8d4830846df676a1dcafb7","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 10, p 562 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/10/562/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11100562","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 11; Issue 10; Pages: 562","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11100562","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11100562","pdf_url":"https://www.mdpi.com/2075-1680/11/10/562/pdf?version=1666594618","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4306403495.pdf","grobid_xml":"https://content.openalex.org/works/W4306403495.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W1256455720","https://openalex.org/W2000954923","https://openalex.org/W2039796408","https://openalex.org/W2156287821","https://openalex.org/W2479014450","https://openalex.org/W2487728874","https://openalex.org/W3215216471","https://openalex.org/W4200161749","https://openalex.org/W4205634890","https://openalex.org/W6683069069","https://openalex.org/W6722717496"],"related_works":["https://openalex.org/W207016472","https://openalex.org/W2361691867","https://openalex.org/W2160832602","https://openalex.org/W2047770421","https://openalex.org/W2326379377","https://openalex.org/W1678170666","https://openalex.org/W4366389222","https://openalex.org/W1982249241","https://openalex.org/W4226069104","https://openalex.org/W4306403495"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2,15,50],"devoted":[3],"to":[4,65,82,103],"a":[5,38],"new":[6,34,114],"first":[7,43],"order":[8,102],"Taylor-like":[9,115],"formula,":[10,35],"where":[11,61],"the":[12,21,27,42,46,58,62,75,78,84,90,97,105,108],"corresponding":[13,85],"remainder":[14],"strongly":[16],"reduced":[17],"in":[18,26,77,101],"comparison":[19],"with":[20],"usual":[22],"one,":[23],"which":[24,49],"appears":[25],"classical":[28],"Taylor\u2019s":[29],"formula.":[30,116],"To":[31],"derive":[32],"this":[33,113],"we":[36,88,110],"introduce":[37],"linear":[39,79],"combination":[40,80],"of":[41,45,74,107],"derivative":[44],"concerned":[47],"function,":[48],"computed":[51],"at":[52],"n+1":[53],"equally":[54],"spaced":[55],"points":[56],"between":[57],"two":[59],"points,":[60],"function":[63],"has":[64],"be":[66],"evaluated.":[67],"We":[68],"show":[69],"that":[70],"an":[71],"optimal":[72],"choice":[73],"weights":[76],"leads":[81],"minimizing":[83],"remainder.":[86],"Then,":[87],"analyze":[89],"Lagrange":[91],"P1-":[92],"interpolation":[93],"error":[94],"estimate":[95],"and":[96],"trapezoidal":[98],"quadrature":[99],"error,":[100],"assess":[104],"gain":[106],"accuracy":[109],"obtain":[111],"using":[112]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2022-10-17T00:00:00"}