{"id":"https://openalex.org/W2011979142","doi":"https://doi.org/10.1080/0020739860170611","title":"A topic in asymptotic approximation","display_name":"A topic in asymptotic approximation","publication_year":1986,"publication_date":"1986-11-01","ids":{"openalex":"https://openalex.org/W2011979142","doi":"https://doi.org/10.1080/0020739860170611","mag":"2011979142"},"language":"en","primary_location":{"id":"doi:10.1080/0020739860170611","doi":"https://doi.org/10.1080/0020739860170611","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0020739860170611","pdf_url":null,"source":{"id":"https://openalex.org/S131125421","display_name":"International Journal of Mathematical Education in Science and Technology","issn_l":"0020-739X","issn":["0020-739X","1464-5211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-1","norway-1"],"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":"International Journal of Mathematical Education in Science and Technology","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/A5110018991","display_name":"R. Shail","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I28290843","display_name":"University of Surrey","ror":"https://ror.org/00ks66431","country_code":"GB","type":"education","lineage":["https://openalex.org/I28290843"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"R. Shail","raw_affiliation_strings":["Department of Mathematics, University of Surrey, Guildford GU2 5XH, Surrey, England","Department of Mathematics , University of Surrey , Guildford GU2 5XH, Surrey, England"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, University of Surrey, Guildford GU2 5XH, Surrey, England","institution_ids":["https://openalex.org/I28290843"]},{"raw_affiliation_string":"Department of Mathematics , University of Surrey , Guildford GU2 5XH, Surrey, England","institution_ids":["https://openalex.org/I28290843"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5110018991"],"corresponding_institution_ids":["https://openalex.org/I28290843"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.23916533,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"17","issue":"6","first_page":"771","last_page":"783"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13806","display_name":"Mathematical and Computational Methods","score":0.5034000277519226,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T13806","display_name":"Mathematical and Computational Methods","score":0.5034000277519226,"subfield":{"id":"https://openalex.org/subfields/2611","display_name":"Modeling and Simulation"},"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/T11191","display_name":"Mathematical functions and polynomials","score":0.4323999881744385,"subfield":{"id":"https://openalex.org/subfields/2604","display_name":"Applied Mathematics"},"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/T12727","display_name":"Differential Equations and Numerical Methods","score":0.013100000098347664,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/asymptotic-approximation","display_name":"asymptotic approximation","score":0.9940000176429749},{"id":"https://openalex.org/keywords/large-n-asymptotics","display_name":"large n asymptotics","score":0.7590000033378601},{"id":"https://openalex.org/keywords/elementary-methods","display_name":"elementary methods","score":0.5910000205039978},{"id":"https://openalex.org/keywords/integral-approximation","display_name":"integral approximation","score":0.5419999957084656}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.559959888458252},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.5259100198745728},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.4629659652709961},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.45012569427490234},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.4430626332759857},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4403139054775238},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2008579969406128},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.18091970682144165},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0677827000617981},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1080/0020739860170611","doi":"https://doi.org/10.1080/0020739860170611","is_oa":false,"landing_page_url":"https://doi.org/10.1080/0020739860170611","pdf_url":null,"source":{"id":"https://openalex.org/S131125421","display_name":"International Journal of Mathematical Education in Science and Technology","issn_l":"0020-739X","issn":["0020-739X","1464-5211"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","erih-plus","jufo-1","norway-1"],"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":"International Journal of Mathematical Education in Science and Technology","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"display_name":"Quality education","id":"https://metadata.un.org/sdg/4","score":0.8500000238418579}],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":10,"referenced_works":["https://openalex.org/W1657347807","https://openalex.org/W2047514744","https://openalex.org/W2057817591","https://openalex.org/W2081338783","https://openalex.org/W2095817904","https://openalex.org/W2120062331","https://openalex.org/W2596323328","https://openalex.org/W2801213956","https://openalex.org/W3119264854","https://openalex.org/W4241483739"],"related_works":["https://openalex.org/W1973641256","https://openalex.org/W2089274067","https://openalex.org/W56994397","https://openalex.org/W1121942432","https://openalex.org/W2418069309","https://openalex.org/W2376158287","https://openalex.org/W1526165314","https://openalex.org/W2359859943","https://openalex.org/W2993306360","https://openalex.org/W2591547446"],"abstract_inverted_index":{"An":[0],"elementary":[1],"method":[2],"is":[3,32],"used":[4],"to":[5,11],"derive":[6],"approximations":[7],"for":[8,45],"large":[9],"N":[10,20],"various":[12],"integrals":[13],"whose":[14],"integrands":[15],"contain":[16],"a":[17,23,29,38],"product":[18],"of":[19,22,28,40],"factors":[21],"prescribed":[24],"form.":[25],"The":[26],"idea":[27],"partial":[30],"expansion":[31],"considered,":[33],"and":[34],"the":[35],"paper":[36],"contains":[37],"collection":[39],"examples":[41],"which":[42],"are":[43],"suitable":[44],"instructional":[46],"purposes.":[47]},"counts_by_year":[],"updated_date":"2026-08-15T07:11:24.734988","created_date":"2025-10-10T00:00:00"}
