{"id":"https://openalex.org/W2082996704","doi":"https://doi.org/10.1142/s021969130900329x","title":"THE COMPLETE ASYMPTOTIC EXPANSIONS FOR THE SZ\u00c1SZ\u2013MIRAKIAN-TYPE OPERATORS","display_name":"THE COMPLETE ASYMPTOTIC EXPANSIONS FOR THE SZ\u00c1SZ\u2013MIRAKIAN-TYPE OPERATORS","publication_year":2009,"publication_date":"2009-11-01","ids":{"openalex":"https://openalex.org/W2082996704","doi":"https://doi.org/10.1142/s021969130900329x","mag":"2082996704"},"language":"en","primary_location":{"id":"doi:10.1142/s021969130900329x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969130900329x","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","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":null,"display_name":"CHUNGOU ZHANG","orcid":null},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"CHUNGOU ZHANG","raw_affiliation_strings":["School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China","School of Mathematical Sciences , Capital Normal University , Beijing 100048 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China","institution_ids":["https://openalex.org/I96852419"]},{"raw_affiliation_string":"School of Mathematical Sciences , Capital Normal University , Beijing 100048 , P. R. China","institution_ids":["https://openalex.org/I96852419"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5015422307","display_name":"QUAN-E WANG","orcid":null},"institutions":[{"id":"https://openalex.org/I96852419","display_name":"Capital Normal University","ror":"https://ror.org/005edt527","country_code":"CN","type":"education","lineage":["https://openalex.org/I96852419"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"QUAN-E WANG","raw_affiliation_strings":["School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China","School of Mathematical Sciences , Capital Normal University , Beijing 100048 , P. R. China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Capital Normal University, Beijing, 100048, P. R. China","institution_ids":["https://openalex.org/I96852419"]},{"raw_affiliation_string":"School of Mathematical Sciences , Capital Normal University , Beijing 100048 , P. R. China","institution_ids":["https://openalex.org/I96852419"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I96852419"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.16788893,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"07","issue":"06","first_page":"851","last_page":"858"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9965999722480774,"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/T11564","display_name":"Mathematical Inequalities and Applications","score":0.9965999722480774,"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/T12062","display_name":"Approximation Theory and Sequence Spaces","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"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":0.9793999791145325,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/asymptotic-expansion","display_name":"Asymptotic expansion","score":0.6823416352272034},{"id":"https://openalex.org/keywords/asymptotic-formula","display_name":"Asymptotic formula","score":0.6046925783157349},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5978477597236633},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.5796836614608765},{"id":"https://openalex.org/keywords/stirling-number","display_name":"Stirling number","score":0.5629798173904419},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"Asymptotic analysis","score":0.5287883877754211},{"id":"https://openalex.org/keywords/operator-theory","display_name":"Operator theory","score":0.42118677496910095},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39072850346565247},{"id":"https://openalex.org/keywords/mathematical-physics","display_name":"Mathematical physics","score":0.3369041383266449},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.3234521150588989},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.2900850772857666},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2496805191040039}],"concepts":[{"id":"https://openalex.org/C11683690","wikidata":"https://www.wikidata.org/wiki/Q752726","display_name":"Asymptotic expansion","level":2,"score":0.6823416352272034},{"id":"https://openalex.org/C24209939","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic formula","level":2,"score":0.6046925783157349},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5978477597236633},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.5796836614608765},{"id":"https://openalex.org/C168902406","wikidata":"https://www.wikidata.org/wiki/Q80918","display_name":"Stirling number","level":2,"score":0.5629798173904419},{"id":"https://openalex.org/C119047807","wikidata":"https://www.wikidata.org/wiki/Q752718","display_name":"Asymptotic analysis","level":2,"score":0.5287883877754211},{"id":"https://openalex.org/C43929395","wikidata":"https://www.wikidata.org/wiki/Q1198874","display_name":"Operator theory","level":2,"score":0.42118677496910095},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39072850346565247},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.3369041383266449},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3234521150588989},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2900850772857666},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2496805191040039},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s021969130900329x","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s021969130900329x","pdf_url":null,"source":{"id":"https://openalex.org/S56986848","display_name":"International Journal of Wavelets Multiresolution and Information Processing","issn_l":"0219-6913","issn":["0219-6913","1793-690X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319815","host_organization_name":"World Scientific","host_organization_lineage":["https://openalex.org/P4310319815"],"host_organization_lineage_names":["World Scientific"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Wavelets, Multiresolution and Information Processing","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.44999998807907104}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":3,"referenced_works":["https://openalex.org/W7967199","https://openalex.org/W1992263716","https://openalex.org/W2079492704"],"related_works":["https://openalex.org/W1491114765","https://openalex.org/W1973839524","https://openalex.org/W4231988990","https://openalex.org/W1985820779","https://openalex.org/W2386096684","https://openalex.org/W2105833598","https://openalex.org/W4298364303","https://openalex.org/W2020088966","https://openalex.org/W2963514792","https://openalex.org/W2102417950"],"abstract_inverted_index":{"This":[0],"paper":[1],"is":[2],"devoted":[3],"to":[4],"exploring":[5],"asymptotic":[6,39],"behavior":[7],"of":[8,23,44,53,62,66],"the":[9,13,37,42,63,67],"Sz\u00e1sz\u2013Mirakian-type":[10],"operators":[11,15],"including":[12],"Sz\u00e1sz\u2013Mirakian":[14],"S":[16],"n":[17,54],"(f;x)":[18,52],"and":[19,69],"its":[20],"two":[21],"kinds":[22],"integral":[24],"modifications":[25],"[Formula:":[26,29,45],"see":[27,30,46],"text],":[28],"text].":[31],"For":[32],"these":[33],"operators,":[34],"we":[35],"obtain":[36],"complete":[38],"expansions":[40],"in":[41,60],"form":[43],"text]":[47],"all":[48],"coefficients":[49],"a":[50],"k":[51],"-k":[55],"(k=1,2,\u2026)":[56],"are":[57],"calculated":[58],"explicitly":[59],"terms":[61],"Stirling":[64],"numbers":[65],"first":[68],"second":[70],"kind.":[71]},"counts_by_year":[],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}