{"id":"https://openalex.org/W4232004208","doi":"https://doi.org/10.1080/00029890.1970.11992475","title":"An Elementary Discussion of the Transcendental Nature of the Elementary Transcendental Functions","display_name":"An Elementary Discussion of the Transcendental Nature of the Elementary Transcendental Functions","publication_year":1970,"publication_date":"1970-03-01","ids":{"openalex":"https://openalex.org/W4232004208","doi":"https://doi.org/10.1080/00029890.1970.11992475"},"language":"en","primary_location":{"id":"doi:10.1080/00029890.1970.11992475","doi":"https://doi.org/10.1080/00029890.1970.11992475","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.1970.11992475","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,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-4","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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"},"volume":null,"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/A5041349015","display_name":"R. W. Hamming","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"R. W. Hamming","raw_affiliation_strings":["Bell Telephone Laboratories"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bell Telephone Laboratories","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":["https://openalex.org/A5041349015"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":3,"citation_normalized_percentile":{"value":0.66262626,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"77","issue":"3","first_page":"294","last_page":"294"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.2874000072479248,"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"}},"topics":[{"id":"https://openalex.org/T12170","display_name":"History and Theory of Mathematics","score":0.2874000072479248,"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"}},{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.2831999957561493,"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/T10061","display_name":"Algebraic Geometry and Number Theory","score":0.11320000141859055,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/transcendental-functions","display_name":"transcendental functions","score":0.8679999709129333},{"id":"https://openalex.org/keywords/transcendence","display_name":"transcendence","score":0.7419999837875366},{"id":"https://openalex.org/keywords/elementary-functions","display_name":"elementary functions","score":0.8669999837875366},{"id":"https://openalex.org/keywords/exponential-function","display_name":"exponential function","score":0.6679999828338623},{"id":"https://openalex.org/keywords/logarithms","display_name":"logarithms","score":0.8880000114440918},{"id":"https://openalex.org/keywords/trigonometric-functions","display_name":"trigonometric functions","score":0.8640000224113464},{"id":"https://openalex.org/keywords/transcendental-number-theory","display_name":"transcendental number theory","score":0.4560000002384186}],"concepts":[{"id":"https://openalex.org/C188370112","wikidata":"https://www.wikidata.org/wiki/Q173091","display_name":"Transcendental number","level":2,"score":0.9448729753494263},{"id":"https://openalex.org/C43321923","wikidata":"https://www.wikidata.org/wiki/Q864333","display_name":"Transcendental function","level":2,"score":0.7989778518676758},{"id":"https://openalex.org/C139609574","wikidata":"https://www.wikidata.org/wiki/Q2273509","display_name":"Transcendental equation","level":3,"score":0.5442027449607849},{"id":"https://openalex.org/C182408441","wikidata":"https://www.wikidata.org/wiki/Q824282","display_name":"Elementary function","level":2,"score":0.4182884395122528},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4176277220249176},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.38443493843078613},{"id":"https://openalex.org/C145420912","wikidata":"https://www.wikidata.org/wiki/Q853077","display_name":"Mathematics education","level":1,"score":0.35279276967048645},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.32681483030319214},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.29431241750717163},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10091090202331543},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.06583067774772644},{"id":"https://openalex.org/C78045399","wikidata":"https://www.wikidata.org/wiki/Q11214","display_name":"Differential equation","level":2,"score":0.033651202917099},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1080/00029890.1970.11992475","doi":"https://doi.org/10.1080/00029890.1970.11992475","is_oa":false,"landing_page_url":"https://doi.org/10.1080/00029890.1970.11992475","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,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-4","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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":"doi:10.2307/2317719","doi":"https://doi.org/10.2307/2317719","is_oa":false,"landing_page_url":"https://doi.org/10.2307/2317719","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,"listed_in":["anvur-scientific","dongbi-b","jufo-1","norway-1","poland-40","russia-white-list-4","vabb-shw"],"host_organization":"https://openalex.org/P4310320547","host_organization_name":"Taylor & Francis","host_organization_lineage":["https://openalex.org/P4310320547","https://openalex.org/P4310320449"],"host_organization_lineage_names":["Taylor & Francis","Informa"],"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"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"score":0.6200000047683716,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W3014029144","https://openalex.org/W2074397670","https://openalex.org/W4300089223","https://openalex.org/W4387814077","https://openalex.org/W2041431871","https://openalex.org/W4378448846","https://openalex.org/W2233678604","https://openalex.org/W3122176387","https://openalex.org/W1500215907","https://openalex.org/W4298092961"],"abstract_inverted_index":null,"counts_by_year":[{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2025-10-10T00:00:00"}