{"id":"https://openalex.org/W2903640518","doi":"https://doi.org/10.3233/asy-181483","title":"On Pizzetti\u2019s formula","display_name":"On Pizzetti\u2019s formula","publication_year":2018,"publication_date":"2018-12-10","ids":{"openalex":"https://openalex.org/W2903640518","doi":"https://doi.org/10.3233/asy-181483","mag":"2903640518"},"language":"en","primary_location":{"id":"doi:10.3233/asy-181483","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-181483","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":true,"oa_status":"green","oa_url":"https://digitalcommons.lsu.edu/mathematics_pubs/265","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5008853427","display_name":"Ricardo Estrada","orcid":"https://orcid.org/0000-0002-9354-3471"},"institutions":[{"id":"https://openalex.org/I121820613","display_name":"Louisiana State University","ror":"https://ror.org/05ect4e57","country_code":"US","type":"education","lineage":["https://openalex.org/I121820613"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Ricardo Estrada","raw_affiliation_strings":["Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA. E-mail:\u00a0","Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA. E-mail:\u00a0restrada@math.lsu.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA. E-mail:\u00a0","institution_ids":["https://openalex.org/I121820613"]},{"raw_affiliation_string":"Department of Mathematics, Louisiana State University, Baton Rouge, LA 70803, USA. E-mail:\u00a0restrada@math.lsu.edu","institution_ids":["https://openalex.org/I121820613"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5008853427"],"corresponding_institution_ids":["https://openalex.org/I121820613"],"apc_list":null,"apc_paid":null,"fwci":1.4592,"has_fulltext":false,"cited_by_count":4,"citation_normalized_percentile":{"value":0.80455938,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"111","issue":"1","first_page":"1","last_page":"14"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T13400","display_name":"Mathematical and Theoretical Analysis","score":0.9998999834060669,"subfield":{"id":"https://openalex.org/subfields/2610","display_name":"Mathematical Physics"},"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/T12170","display_name":"History and Theory of Mathematics","score":0.9965999722480774,"subfield":{"id":"https://openalex.org/subfields/2614","display_name":"Theoretical Computer Science"},"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/T12508","display_name":"Functional Equations Stability Results","score":0.9954000115394592,"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/mathematics","display_name":"Mathematics","score":0.3984050750732422},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.32881709933280945}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3984050750732422},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.32881709933280945}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3233/asy-181483","is_oa":false,"landing_page_url":"https://doi.org/10.3233/asy-181483","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"},{"id":"pmh:oai:digitalcommons.lsu.edu:mathematics_pubs-1264","is_oa":true,"landing_page_url":"https://digitalcommons.lsu.edu/mathematics_pubs/265","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},{"id":"pmh:oai:repository.lsu.edu:mathematics_pubs-1264","is_oa":true,"landing_page_url":"https://repository.lsu.edu/mathematics_pubs/265","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:digitalcommons.lsu.edu:mathematics_pubs-1264","is_oa":true,"landing_page_url":"https://digitalcommons.lsu.edu/mathematics_pubs/265","pdf_url":null,"source":{"id":"https://openalex.org/S4210169993","display_name":"Civil War Book Review","issn_l":"1528-6592","issn":["1528-6592"],"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/P4310315936","host_organization_name":"Louisiana State University","host_organization_lineage":["https://openalex.org/P4310315936"],"host_organization_lineage_names":["Louisiana State University"],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Faculty Publications","raw_type":"text"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W161595128","https://openalex.org/W592066523","https://openalex.org/W635890191","https://openalex.org/W1533055209","https://openalex.org/W1538706232","https://openalex.org/W1965738715","https://openalex.org/W2003930968","https://openalex.org/W2014678906","https://openalex.org/W2020448344","https://openalex.org/W2075085615","https://openalex.org/W2123194815","https://openalex.org/W2163405062","https://openalex.org/W2415691143","https://openalex.org/W2518915563","https://openalex.org/W2781908238","https://openalex.org/W3022664448","https://openalex.org/W3092392916","https://openalex.org/W3105473514","https://openalex.org/W4206110393","https://openalex.org/W4230266154","https://openalex.org/W4300133707","https://openalex.org/W4300793121"],"related_works":["https://openalex.org/W2935759653","https://openalex.org/W3105167352","https://openalex.org/W54078636","https://openalex.org/W2954470139","https://openalex.org/W1501425562","https://openalex.org/W2902782467","https://openalex.org/W3084825885","https://openalex.org/W2298861036","https://openalex.org/W3148032049","https://openalex.org/W2271181815"],"abstract_inverted_index":{"We":[0,60,76,128],"give":[1],"an":[2,16,91],"extended":[3],"Pizzetti":[4],"asymptotic":[5],"formula,":[6],"namely,":[7],"we":[8],"show":[9,62,113],"that":[10,19,54,63,103,114,147],"if":[11,28,71],"\u03d5":[12],"is":[13,30,73,104],"smooth":[14,100],"in":[15,23,57],"open":[17],"set":[18],"contains":[20],"the":[21,58,64,83,88,115,119],"origin":[22],"[Formula:":[24,39,43,51],"see":[25,40,44,52],"text]":[26,41,45,53],"and":[27,50,82,112],"p":[29,72],"a":[31,94,99,105,109,142],"harmonic":[32,123],"homogeneous":[33],"polynomial":[34,111],"of":[35,90,108,137,144],"degree":[36],"k,":[37],"then":[38],"as":[42],"for":[46,68,122,135],"some":[47],"constants":[48],"C":[49],"are":[55],"given":[56,110],"text.":[59],"also":[61,129],"formula":[65],"never":[66],"holds,":[67],"all":[69],"\u03d5,":[70],"not":[74,126],"harmonic.":[75],"consider":[77,130],"two":[78,116],"procedures,":[79],"one":[80],"algebraic":[81],"other":[84],"analytic,":[85],"to":[86,149],"find":[87],"part":[89],"object":[92],"\u2013":[93,102],"formal":[95],"power":[96],"series":[97],"or":[98],"function":[101],"radial":[106],"multiple":[107],"constructions":[117],"yield":[118],"same":[120],"results":[121,134],"polynomials":[124],"but":[125],"otherwise.":[127],"mean":[131],"value":[132],"type":[133],"solutions":[136],"partial":[138],"differential":[139],"equations,":[140],"including":[141],"version":[143],"Morera\u2019s":[145],"theorem":[146],"applies":[148],"locally":[150],"integrable":[151],"functions.":[152]},"counts_by_year":[{"year":2021,"cited_by_count":1},{"year":2020,"cited_by_count":2},{"year":2019,"cited_by_count":1}],"updated_date":"2026-04-30T06:05:26.967640","created_date":"2025-10-10T00:00:00"}