{"id":"https://openalex.org/W1931193966","doi":"https://doi.org/10.3233/asy-2010-1016","title":"Higher asymptotics of Laplace's approximation","display_name":"Higher asymptotics of Laplace's approximation","publication_year":2010,"publication_date":"2010-12-01","ids":{"openalex":"https://openalex.org/W1931193966","doi":"https://doi.org/10.3233/asy-2010-1016","mag":"1931193966"},"language":"en","primary_location":{"id":"doi:10.3233/asy-2010-1016","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2010-1016","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","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/A5018733232","display_name":"William D. Kirwin","orcid":null},"institutions":[{"id":"https://openalex.org/I121345201","display_name":"Instituto de Engenharia de Sistemas e Computadores Investiga\u00e7\u00e3o e Desenvolvimento","ror":"https://ror.org/04mqy3p58","country_code":"PT","type":"nonprofit","lineage":["https://openalex.org/I121345201","https://openalex.org/I4210125590"]},{"id":"https://openalex.org/I149899117","display_name":"Max Planck Society","ror":"https://ror.org/01hhn8329","country_code":"DE","type":"nonprofit","lineage":["https://openalex.org/I149899117"]}],"countries":["DE","PT"],"is_corresponding":true,"raw_author_name":"William D. Kirwin","raw_affiliation_strings":["Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior T\u00e9cnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal. E-mail: will.kirwin@gmail.com","Max Planck Society"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Mathematical Analysis, Geometry and Dynamical Systems, Instituto Superior T\u00e9cnico, Av. Rovisco Pais, 1049-001, Lisbon, Portugal. E-mail: will.kirwin@gmail.com","institution_ids":["https://openalex.org/I121345201"]},{"raw_affiliation_string":"Max Planck Society","institution_ids":["https://openalex.org/I149899117"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5018733232"],"corresponding_institution_ids":["https://openalex.org/I121345201","https://openalex.org/I149899117"],"apc_list":null,"apc_paid":null,"fwci":1.2342,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.74461601,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"70","issue":"3-4","first_page":"231","last_page":"248"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9987000226974487,"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"}},"topics":[{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9987000226974487,"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/T12037","display_name":"Algebraic and Geometric Analysis","score":0.991599977016449,"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9912999868392944,"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/laplace-transform","display_name":"Laplace transform","score":0.7851855158805847},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.7626289129257202},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7296192646026611},{"id":"https://openalex.org/keywords/laplaces-method","display_name":"Laplace's method","score":0.6831910014152527},{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.5981705188751221},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.5209704041481018},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.520869255065918},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.5150177478790283},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.4147215187549591},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4053942561149597},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09144726395606995}],"concepts":[{"id":"https://openalex.org/C97937538","wikidata":"https://www.wikidata.org/wiki/Q199691","display_name":"Laplace transform","level":2,"score":0.7851855158805847},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.7626289129257202},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7296192646026611},{"id":"https://openalex.org/C22243797","wikidata":"https://www.wikidata.org/wiki/Q2058297","display_name":"Laplace's method","level":3,"score":0.6831910014152527},{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.5981705188751221},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.5209704041481018},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.520869255065918},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.5150177478790283},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.4147215187549591},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4053942561149597},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09144726395606995},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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":1,"locations":[{"id":"doi:10.3233/asy-2010-1016","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-2010-1016","pdf_url":null,"source":{"id":"https://openalex.org/S141283892","display_name":"Asymptotic Analysis","issn_l":"0921-7134","issn":["0921-7134","1875-8576"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310318577","host_organization_name":"IOS Press","host_organization_lineage":["https://openalex.org/P4310318577"],"host_organization_lineage_names":["IOS Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Asymptotic Analysis","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":19,"referenced_works":["https://openalex.org/W1549451790","https://openalex.org/W1996160600","https://openalex.org/W1999769295","https://openalex.org/W2009487014","https://openalex.org/W2017808716","https://openalex.org/W2019915558","https://openalex.org/W2027677127","https://openalex.org/W2049742940","https://openalex.org/W2049948787","https://openalex.org/W2064405705","https://openalex.org/W2084507426","https://openalex.org/W2088469973","https://openalex.org/W2094438648","https://openalex.org/W2157005274","https://openalex.org/W2167266655","https://openalex.org/W2170706425","https://openalex.org/W2317430034","https://openalex.org/W2325699559","https://openalex.org/W2801179766"],"related_works":["https://openalex.org/W2887005408","https://openalex.org/W3035664867","https://openalex.org/W4289676468","https://openalex.org/W4287756321","https://openalex.org/W2041486430","https://openalex.org/W3114582462","https://openalex.org/W2049303112","https://openalex.org/W2407194592","https://openalex.org/W4225727015","https://openalex.org/W4238232493"],"abstract_inverted_index":{"We":[0,66],"present":[1],"expressions":[2,53],"for":[3,79,108],"the":[4,33,36,46,49,52,80,84,87,94,102,109],"coefficients":[5],"which":[6,21,58,71],"arise":[7],"in":[8,27,35,64,86],"asymptotic":[9,30],"expansions":[10],"of":[11,14,20,29,32,45,48],"multiple":[12],"integrals":[13,57,103],"Laplace":[15],"type":[16],"(the":[17],"first":[18],"term":[19],"is":[22],"known":[23],"as":[24],"Laplace's":[25],"approximation)":[26],"terms":[28],"series":[31,92],"functions":[34,47,85],"integrand.":[37],"Our":[38],"most":[39],"general":[40],"result":[41],"assumes":[42],"no":[43],"smoothness":[44],"integrand,":[50],"but":[51],"we":[54,100],"obtain":[55,105],"contain":[56],"may":[59],"be":[60],"difficult":[61],"to":[62,74,104],"evaluate":[63,101],"practice.":[65],"then":[67],"discuss":[68],"additional":[69],"assumptions":[70],"are":[72],"sufficient":[73],"simplify":[75],"these":[76],"integrals,":[77],"and":[78,93],"common":[81],"case":[82],"that":[83],"integrand":[88],"admit":[89],"(finite)":[90],"Taylor":[91],"exponent":[95],"has":[96],"a":[97],"nondegenerate":[98],"minimum,":[99],"explicit":[106],"formulae":[107],"coefficients.":[110]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-30T06:05:26.967640","created_date":"2025-10-10T00:00:00"}
