{"id":"https://openalex.org/W2004585365","doi":"https://doi.org/10.1137/s0895480102401119","title":"Stirling Numbers for Complex Arguments: Asymptotics and Identities","display_name":"Stirling Numbers for Complex Arguments: Asymptotics and Identities","publication_year":2003,"publication_date":"2003-01-01","ids":{"openalex":"https://openalex.org/W2004585365","doi":"https://doi.org/10.1137/s0895480102401119","mag":"2004585365"},"language":"en","primary_location":{"id":"doi:10.1137/s0895480102401119","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480102401119","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","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/A5037513427","display_name":"Graeme Kemkes","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Graeme Kemkes","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060895665","display_name":"Chiu Fan Lee","orcid":"https://orcid.org/0000-0003-4363-9050"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chiu Fan Lee","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5089697248","display_name":"Donatella Merlini","orcid":"https://orcid.org/0000-0001-8109-4077"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Donatella Merlini","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5051530602","display_name":"Bruce M. Richmond","orcid":"https://orcid.org/0000-0002-0056-5832"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bruce Richmond","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.6994,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.79306609,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":94},"biblio":{"volume":"16","issue":"2","first_page":"179","last_page":"191"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9995999932289124,"subfield":{"id":"https://openalex.org/subfields/2602","display_name":"Algebra and Number Theory"},"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9984999895095825,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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":0.9947999715805054,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/stirling-number","display_name":"Stirling number","score":0.8941538333892822},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-first-kind","display_name":"Stirling numbers of the first kind","score":0.8907155990600586},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.8726148009300232},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-second-kind","display_name":"Stirling numbers of the second kind","score":0.8526465892791748},{"id":"https://openalex.org/keywords/bell-polynomials","display_name":"Bell polynomials","score":0.694132387638092},{"id":"https://openalex.org/keywords/stirling-engine","display_name":"Stirling engine","score":0.5941635966300964},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39047154784202576},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.37535715103149414},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34209662675857544},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32118135690689087}],"concepts":[{"id":"https://openalex.org/C168902406","wikidata":"https://www.wikidata.org/wiki/Q80918","display_name":"Stirling number","level":2,"score":0.8941538333892822},{"id":"https://openalex.org/C93765064","wikidata":"https://www.wikidata.org/wiki/Q2657556","display_name":"Stirling numbers of the first kind","level":3,"score":0.8907155990600586},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.8726148009300232},{"id":"https://openalex.org/C2284495","wikidata":"https://www.wikidata.org/wiki/Q2601117","display_name":"Stirling numbers of the second kind","level":2,"score":0.8526465892791748},{"id":"https://openalex.org/C154485487","wikidata":"https://www.wikidata.org/wiki/Q815666","display_name":"Bell polynomials","level":2,"score":0.694132387638092},{"id":"https://openalex.org/C27134321","wikidata":"https://www.wikidata.org/wiki/Q186212","display_name":"Stirling engine","level":2,"score":0.5941635966300964},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39047154784202576},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.37535715103149414},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34209662675857544},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32118135690689087},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1137/s0895480102401119","is_oa":false,"landing_page_url":"https://doi.org/10.1137/s0895480102401119","pdf_url":null,"source":{"id":"https://openalex.org/S117679221","display_name":"SIAM Journal on Discrete Mathematics","issn_l":"0895-4801","issn":["0895-4801","1095-7146"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320508","host_organization_name":"Society for Industrial and Applied Mathematics","host_organization_lineage":["https://openalex.org/P4310320508"],"host_organization_lineage_names":["Society for Industrial and Applied Mathematics"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"SIAM Journal on Discrete Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:flore.unifi.it:2158/312507","is_oa":false,"landing_page_url":"http://hdl.handle.net/2158/312507","pdf_url":null,"source":{"id":"https://openalex.org/S4306402033","display_name":"Florence Research (University of Florence)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I45084792","host_organization_name":"University of Florence","host_organization_lineage":["https://openalex.org/I45084792"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","score":0.4300000071525574,"display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":13,"referenced_works":["https://openalex.org/W587894314","https://openalex.org/W2006524576","https://openalex.org/W2039343706","https://openalex.org/W2057817591","https://openalex.org/W2065937368","https://openalex.org/W2072577284","https://openalex.org/W2079808805","https://openalex.org/W2088627906","https://openalex.org/W2133006861","https://openalex.org/W2144065122","https://openalex.org/W3037257960","https://openalex.org/W4212799367","https://openalex.org/W4240867252"],"related_works":["https://openalex.org/W3112509002","https://openalex.org/W3108596636","https://openalex.org/W2764183459","https://openalex.org/W2235095426","https://openalex.org/W2983326473","https://openalex.org/W2799775110","https://openalex.org/W4385723703","https://openalex.org/W2367819968","https://openalex.org/W3124765623","https://openalex.org/W2003315419"],"abstract_inverted_index":{"We":[0,17],"derive":[1],"asymptotic":[2],"expansions":[3],"for":[4,23],"the":[5],"Stirling":[6,24],"numbers":[7,25],"of":[8],"real":[9,30],"arguments":[10,28],"as":[11],"defined":[12],"by":[13],"Flajolet":[14],"and":[15],"Prodinger.":[16],"also":[18],"generalize":[19],"certain":[20],"classical":[21],"identities":[22],"with":[26],"integral":[27],"to":[29],"or":[31],"complex":[32],"arguments.":[33]},"counts_by_year":[{"year":2015,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2016-06-24T00:00:00"}
