{"id":"https://openalex.org/W2008453528","doi":"https://doi.org/10.1155/2014/354053","title":"Asymptotic Estimates forr-Whitney Numbers of the Second Kind","display_name":"Asymptotic Estimates forr-Whitney Numbers of the Second Kind","publication_year":2014,"publication_date":"2014-01-01","ids":{"openalex":"https://openalex.org/W2008453528","doi":"https://doi.org/10.1155/2014/354053","mag":"2008453528"},"language":"en","primary_location":{"id":"doi:10.1155/2014/354053","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/354053","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/354053.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://downloads.hindawi.com/journals/jam/2014/354053.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003324386","display_name":"Cristina B. Corcino","orcid":"https://orcid.org/0000-0003-1634-9605"},"institutions":[{"id":"https://openalex.org/I87074743","display_name":"University of the Philippines Diliman","ror":"https://ror.org/03tbh6y23","country_code":"PH","type":"education","lineage":["https://openalex.org/I103911934","https://openalex.org/I87074743"]}],"countries":["PH"],"is_corresponding":false,"raw_author_name":"Cristina B. Corcino","raw_affiliation_strings":["Institute of Mathematics, University of the Philippines, Diliman, 1101 Quezon City, Philippines"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute of Mathematics, University of the Philippines, Diliman, 1101 Quezon City, Philippines","institution_ids":["https://openalex.org/I87074743"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039827279","display_name":"Roberto B. Corcino","orcid":"https://orcid.org/0000-0003-1681-1804"},"institutions":[{"id":"https://openalex.org/I354071399","display_name":"Mindanao State University","ror":"https://ror.org/026441d17","country_code":"PH","type":"education","lineage":["https://openalex.org/I354071399"]}],"countries":["PH"],"is_corresponding":true,"raw_author_name":"Roberto B. Corcino","raw_affiliation_strings":["Department of Mathematics, Mindanao State University, 9700 Marawi City, Philippines"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mindanao State University, 9700 Marawi City, Philippines","institution_ids":["https://openalex.org/I354071399"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5072763694","display_name":"Nestor G. Acala","orcid":"https://orcid.org/0000-0003-1003-7248"},"institutions":[{"id":"https://openalex.org/I354071399","display_name":"Mindanao State University","ror":"https://ror.org/026441d17","country_code":"PH","type":"education","lineage":["https://openalex.org/I354071399"]}],"countries":["PH"],"is_corresponding":false,"raw_author_name":"Nestor Acala","raw_affiliation_strings":["Department of Mathematics, Mindanao State University, 9700 Marawi City, Philippines"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Mindanao State University, 9700 Marawi City, Philippines","institution_ids":["https://openalex.org/I354071399"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5039827279"],"corresponding_institution_ids":["https://openalex.org/I354071399"],"apc_list":{"value":1130,"currency":"USD","value_usd":1130},"apc_paid":{"value":1130,"currency":"USD","value_usd":1130},"fwci":6.2091,"has_fulltext":true,"cited_by_count":16,"citation_normalized_percentile":{"value":0.97279342,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"2014","issue":null,"first_page":"1","last_page":"7"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991000294685364,"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"}},"topics":[{"id":"https://openalex.org/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9991000294685364,"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/T11428","display_name":"Advanced Mathematical Identities","score":0.9991000294685364,"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/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.8003976345062256},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.788905143737793},{"id":"https://openalex.org/keywords/integer","display_name":"Integer (computer science)","score":0.6803891658782959},{"id":"https://openalex.org/keywords/real-line","display_name":"Real line","score":0.6509720683097839},{"id":"https://openalex.org/keywords/stirling-number","display_name":"Stirling number","score":0.5125577449798584},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-first-kind","display_name":"Stirling numbers of the first kind","score":0.5031306147575378},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4950043559074402},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.49320119619369507},{"id":"https://openalex.org/keywords/stirling-numbers-of-the-second-kind","display_name":"Stirling numbers of the second kind","score":0.46071797609329224},{"id":"https://openalex.org/keywords/line","display_name":"Line (geometry)","score":0.45619067549705505},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"Asymptotic formula","score":0.4403917193412781},{"id":"https://openalex.org/keywords/real-number","display_name":"Real number","score":0.42966774106025696},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3541403114795685},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33913201093673706},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.21824917197227478},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.0762501060962677},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.050704240798950195}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.8003976345062256},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.788905143737793},{"id":"https://openalex.org/C97137487","wikidata":"https://www.wikidata.org/wiki/Q729138","display_name":"Integer (computer science)","level":2,"score":0.6803891658782959},{"id":"https://openalex.org/C75432250","wikidata":"https://www.wikidata.org/wiki/Q29654355","display_name":"Real line","level":2,"score":0.6509720683097839},{"id":"https://openalex.org/C168902406","wikidata":"https://www.wikidata.org/wiki/Q80918","display_name":"Stirling number","level":2,"score":0.5125577449798584},{"id":"https://openalex.org/C93765064","wikidata":"https://www.wikidata.org/wiki/Q2657556","display_name":"Stirling numbers of the first kind","level":3,"score":0.5031306147575378},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4950043559074402},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.49320119619369507},{"id":"https://openalex.org/C2284495","wikidata":"https://www.wikidata.org/wiki/Q2601117","display_name":"Stirling numbers of the second kind","level":2,"score":0.46071797609329224},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.45619067549705505},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.4403917193412781},{"id":"https://openalex.org/C94020503","wikidata":"https://www.wikidata.org/wiki/Q12916","display_name":"Real number","level":2,"score":0.42966774106025696},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3541403114795685},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33913201093673706},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.21824917197227478},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0762501060962677},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.050704240798950195},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","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},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1155/2014/354053","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/354053","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/354053.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},{"id":"pmh:oai:CULeuclid:euclid.jam/1425305526","is_oa":false,"landing_page_url":"https://projecteuclid.org/euclid.jam/1425305526","pdf_url":null,"source":{"id":"https://openalex.org/S4306400787","display_name":"Project Euclid (Cornell University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Text"},{"id":"pmh:oai:doaj.org/article:752bd779792a4a0ab0916ba591411070","is_oa":true,"landing_page_url":"https://doaj.org/article/752bd779792a4a0ab0916ba591411070","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Journal of Applied Mathematics, Vol 2014 (2014)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1155/2014/354053","is_oa":true,"landing_page_url":"https://doi.org/10.1155/2014/354053","pdf_url":"https://downloads.hindawi.com/journals/jam/2014/354053.pdf","source":{"id":"https://openalex.org/S190082376","display_name":"Journal of Applied Mathematics","issn_l":"1110-757X","issn":["1110-757X","1687-0042"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310319869","host_organization_name":"Hindawi Publishing Corporation","host_organization_lineage":["https://openalex.org/P4310319869","https://openalex.org/P4310320595"],"host_organization_lineage_names":["Hindawi Publishing Corporation","Wiley"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Journal of Applied Mathematics","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2008453528.pdf","grobid_xml":"https://content.openalex.org/works/W2008453528.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W123151599","https://openalex.org/W1970868013","https://openalex.org/W1978468047","https://openalex.org/W2006209383","https://openalex.org/W2060785905","https://openalex.org/W2079808805","https://openalex.org/W2116387389","https://openalex.org/W2136169238","https://openalex.org/W2337068693","https://openalex.org/W2962986399","https://openalex.org/W3176886010"],"related_works":["https://openalex.org/W1644555362","https://openalex.org/W2146355527","https://openalex.org/W2153676633","https://openalex.org/W4322832209","https://openalex.org/W4304776914","https://openalex.org/W2441714773","https://openalex.org/W2081524161","https://openalex.org/W4309828084","https://openalex.org/W2116387389","https://openalex.org/W3043616710"],"abstract_inverted_index":{"Ther-Whitney":[0],"numbers":[1,13,36],"of":[2,9,14,26,37,51,53],"the":[3,11,15,23,38,49],"second":[4,16,39],"kind":[5,17,40],"are":[6,19,46],"a":[7],"generalization":[8,25],"all":[10],"Stirling-type":[12],"which":[18],"in":[20],"line":[21],"with":[22,41],"unified":[24],"Hsu":[27],"and":[28,43,48],"Shuie.":[29],"In":[30],"this":[31],"paper,":[32],"asymptotic":[33],"formulas":[34],"forr-Whitney":[35],"integer":[42],"real":[44],"parameters":[45],"obtained":[47],"range":[50],"validity":[52],"each":[54],"formula":[55],"is":[56],"established.":[57]},"counts_by_year":[{"year":2022,"cited_by_count":1},{"year":2018,"cited_by_count":3},{"year":2016,"cited_by_count":5},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":5}],"updated_date":"2026-08-21T09:56:20.448147","created_date":"2016-06-24T00:00:00"}
