{"id":"https://openalex.org/W3093751157","doi":"https://doi.org/10.1080/00029890.2020.1803627","title":"A Short, Elementary Introduction to the Exponential Function","display_name":"A Short, Elementary Introduction to the Exponential Function","publication_year":2020,"publication_date":"2020-10-20","ids":{"openalex":"https://openalex.org/W3093751157","doi":"https://doi.org/10.1080/00029890.2020.1803627","mag":"3093751157"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.2020.1803627","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1803627","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","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/A5088225535","display_name":"Vilmos Komornik","orcid":"https://orcid.org/0000-0001-8061-7374"},"institutions":[{"id":"https://openalex.org/I68947357","display_name":"Universit\u00e9 de Strasbourg","ror":"https://ror.org/00pg6eq24","country_code":"FR","type":"education","lineage":["https://openalex.org/I68947357"]}],"countries":["FR"],"is_corresponding":true,"raw_author_name":"Vilmos Komornik","raw_affiliation_strings":["D\u00e9partement de Math\u00e9matique, Universit\u00e9 de Strasbourg, 7 rue Ren\u00e9 Descartes, 67084 Strasbourg Cedex, France"],"affiliations":[{"raw_affiliation_string":"D\u00e9partement de Math\u00e9matique, Universit\u00e9 de Strasbourg, 7 rue Ren\u00e9 Descartes, 67084 Strasbourg Cedex, France","institution_ids":["https://openalex.org/I68947357"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5088225535"],"corresponding_institution_ids":["https://openalex.org/I68947357"],"apc_list":null,"apc_paid":null,"fwci":0.589,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.65116834,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"127","issue":"9","first_page":"841","last_page":"846"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9736999869346619,"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":0.9736999869346619,"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/T12504","display_name":"Mathematics and Applications","score":0.9596999883651733,"subfield":{"id":"https://openalex.org/subfields/2608","display_name":"Geometry and Topology"},"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":0.9118000268936157,"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/exponential-function","display_name":"Exponential function","score":0.7010327577590942},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.6642634272575378},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5912257432937622},{"id":"https://openalex.org/keywords/elementary-function","display_name":"Elementary function","score":0.5749609470367432},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5608479380607605},{"id":"https://openalex.org/keywords/convergent-series","display_name":"Convergent series","score":0.43837684392929077},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.43384116888046265},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4223494529724121},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3731311559677124},{"id":"https://openalex.org/keywords/calculus","display_name":"Calculus (dental)","score":0.3722727298736572},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2748759090900421},{"id":"https://openalex.org/keywords/power-series","display_name":"Power series","score":0.09850361943244934},{"id":"https://openalex.org/keywords/medicine","display_name":"Medicine","score":0.050851792097091675}],"concepts":[{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.7010327577590942},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.6642634272575378},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5912257432937622},{"id":"https://openalex.org/C182408441","wikidata":"https://www.wikidata.org/wiki/Q824282","display_name":"Elementary function","level":2,"score":0.5749609470367432},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5608479380607605},{"id":"https://openalex.org/C1115519","wikidata":"https://www.wikidata.org/wiki/Q1211057","display_name":"Convergent series","level":3,"score":0.43837684392929077},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.43384116888046265},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4223494529724121},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3731311559677124},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3722727298736572},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2748759090900421},{"id":"https://openalex.org/C73905626","wikidata":"https://www.wikidata.org/wiki/Q206925","display_name":"Power series","level":2,"score":0.09850361943244934},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.050851792097091675},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","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/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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00029890.2020.1803627","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.2020.1803627","pdf_url":null,"source":{"id":"https://openalex.org/S156280010","display_name":"American Mathematical Monthly","issn_l":"0002-9890","issn":["0002-9890","1930-0972"],"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547"],"host_organization_lineage_names":["Taylor & Francis"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The American Mathematical Monthly","raw_type":"journal-article"},{"id":"pmh:oai:HAL:hal-03529882v1","is_oa":false,"landing_page_url":"https://hal.science/hal-03529882","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"The American Mathematical Monthly, 2020, 127 (9), pp.841-846. ⟨10.1080/00029890.2020.1803627⟩","raw_type":"Journal articles"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.6700000166893005,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":9,"referenced_works":["https://openalex.org/W1538508619","https://openalex.org/W1969304434","https://openalex.org/W1991523795","https://openalex.org/W2079509440","https://openalex.org/W2135853734","https://openalex.org/W2328264916","https://openalex.org/W2328504504","https://openalex.org/W2600879927","https://openalex.org/W4230227726"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W2014991381","https://openalex.org/W2796943335","https://openalex.org/W138297200","https://openalex.org/W2884146757","https://openalex.org/W1981383328"],"abstract_inverted_index":{"We":[0],"give":[1],"a":[2],"short":[3],"construction":[4],"of":[5,14],"the":[6,11],"exponential":[7],"function":[8],"using":[9],"only":[10],"simplest":[12],"properties":[13],"convergent":[15,36],"sequences":[16],"and":[17],"two":[18],"well-known":[19],"elementary":[20],"inequalities.":[21],"It":[22],"could":[23],"be":[24],"used":[25],"at":[26],"an":[27],"early":[28],"stage":[29],"in":[30],"introductory":[31],"analysis":[32],"courses,":[33],"before":[34],"studying":[35],"series,":[37],"continuity,":[38],"or":[39],"differentiability.":[40]},"counts_by_year":[{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}