{"id":"https://openalex.org/W3147458306","doi":"https://doi.org/10.3390/axioms10020051","title":"Pseudo-Lucas Functions of Fractional Degree and Applications","display_name":"Pseudo-Lucas Functions of Fractional Degree and Applications","publication_year":2021,"publication_date":"2021-04-02","ids":{"openalex":"https://openalex.org/W3147458306","doi":"https://doi.org/10.3390/axioms10020051","mag":"3147458306"},"language":"en","primary_location":{"id":"doi:10.3390/axioms10020051","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10020051","pdf_url":"https://www.mdpi.com/2075-1680/10/2/51/pdf?version=1617939751","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2075-1680/10/2/51/pdf?version=1617939751","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5080017749","display_name":"Clemente Cesarano","orcid":"https://orcid.org/0000-0002-1694-7907"},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Clemente Cesarano","raw_affiliation_strings":["Section of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II. 39, 00186 Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Section of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II. 39, 00186 Rome, Italy","institution_ids":["https://openalex.org/I4210155399"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5046705553","display_name":"Pierpaolo Natalini","orcid":"https://orcid.org/0000-0002-3862-8376"},"institutions":[{"id":"https://openalex.org/I119003972","display_name":"Roma Tre University","ror":"https://ror.org/05vf0dg29","country_code":"IT","type":"education","lineage":["https://openalex.org/I119003972"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Pierpaolo Natalini","raw_affiliation_strings":["Department of Mathematics and Physics, Roma Tre University, Largo San Leonardo Murialdo, 1, 00146 Rome, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics and Physics, Roma Tre University, Largo San Leonardo Murialdo, 1, 00146 Rome, Italy","institution_ids":["https://openalex.org/I119003972"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5087019684","display_name":"Paolo Emilio Ricci","orcid":"https://orcid.org/0000-0002-7899-3087"},"institutions":[{"id":"https://openalex.org/I4210155399","display_name":"UniNettuno University","ror":"https://ror.org/04q0nep37","country_code":"IT","type":"education","lineage":["https://openalex.org/I4210155399"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Paolo Ricci","raw_affiliation_strings":["Section of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II. 39, 00186 Rome, Italy"],"raw_orcid":"https://orcid.org/0000-0002-7899-3087","affiliations":[{"raw_affiliation_string":"Section of Mathematics, International Telematic University UniNettuno, Corso Vittorio Emanuele II. 39, 00186 Rome, Italy","institution_ids":["https://openalex.org/I4210155399"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5080017749"],"corresponding_institution_ids":["https://openalex.org/I4210155399"],"apc_list":{"value":1600,"currency":"CHF","value_usd":1782},"apc_paid":{"value":1600,"currency":"CHF","value_usd":1782},"fwci":0.6956,"has_fulltext":true,"cited_by_count":6,"citation_normalized_percentile":{"value":0.66886204,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":95,"max":97},"biblio":{"volume":"10","issue":"2","first_page":"51","last_page":"51"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9998000264167786,"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"}},"topics":[{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9998000264167786,"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"}},{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":0.9865000247955322,"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/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9861000180244446,"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/mathematics","display_name":"Mathematics","score":0.7045440077781677},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.686244010925293},{"id":"https://openalex.org/keywords/degree","display_name":"Degree (music)","score":0.6638058423995972},{"id":"https://openalex.org/keywords/representation","display_name":"Representation (politics)","score":0.5414076447486877},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.5083054900169373},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.48689380288124084},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4526996612548828},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.44375932216644287},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.43933409452438354},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.42046481370925903},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.41962867975234985},{"id":"https://openalex.org/keywords/chebyshev-nodes","display_name":"Chebyshev nodes","score":0.41139882802963257},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3522631525993347},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.2595594525337219},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.14950966835021973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7045440077781677},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.686244010925293},{"id":"https://openalex.org/C2775997480","wikidata":"https://www.wikidata.org/wiki/Q586277","display_name":"Degree (music)","level":2,"score":0.6638058423995972},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.5414076447486877},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.5083054900169373},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.48689380288124084},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4526996612548828},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.44375932216644287},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.43933409452438354},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.42046481370925903},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.41962867975234985},{"id":"https://openalex.org/C171326582","wikidata":"https://www.wikidata.org/wiki/Q1052508","display_name":"Chebyshev nodes","level":3,"score":0.41139882802963257},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3522631525993347},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.2595594525337219},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.14950966835021973},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C94625758","wikidata":"https://www.wikidata.org/wiki/Q7163","display_name":"Politics","level":2,"score":0.0},{"id":"https://openalex.org/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"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/C24890656","wikidata":"https://www.wikidata.org/wiki/Q82811","display_name":"Acoustics","level":1,"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":4,"locations":[{"id":"doi:10.3390/axioms10020051","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10020051","pdf_url":"https://www.mdpi.com/2075-1680/10/2/51/pdf?version=1617939751","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:6a82111cb2834952a26bd49556363442","is_oa":false,"landing_page_url":"https://doaj.org/article/6a82111cb2834952a26bd49556363442","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 10, Iss 2, p 51 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/10/2/51/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms10020051","pdf_url":null,"source":{"id":"https://openalex.org/S4306400947","display_name":"MDPI (MDPI AG)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210097602","host_organization_name":"Multidisciplinary Digital Publishing Institute (Switzerland)","host_organization_lineage":["https://openalex.org/I4210097602"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms; Volume 10; Issue 2; Pages: 51","raw_type":"Text"},{"id":"pmh:oai:zenodo.org:160586","is_oa":true,"landing_page_url":"https://www.openaccessrepository.it/record/160586","pdf_url":null,"source":{"id":"https://openalex.org/S4306402478","display_name":"INFM-OAR (INFN Catania)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I4210116497","host_organization_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Catania","host_organization_lineage":["https://openalex.org/I4210116497"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"}],"best_oa_location":{"id":"doi:10.3390/axioms10020051","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms10020051","pdf_url":"https://www.mdpi.com/2075-1680/10/2/51/pdf?version=1617939751","source":{"id":"https://openalex.org/S4210173132","display_name":"Axioms","issn_l":"2075-1680","issn":["2075-1680"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Axioms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3147458306.pdf","grobid_xml":"https://content.openalex.org/works/W3147458306.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W180973370","https://openalex.org/W1480654803","https://openalex.org/W1530983653","https://openalex.org/W1549500029","https://openalex.org/W1987218781","https://openalex.org/W2014890084","https://openalex.org/W2017696690","https://openalex.org/W2019559203","https://openalex.org/W2038232928","https://openalex.org/W2045497314","https://openalex.org/W2046578760","https://openalex.org/W2052064203","https://openalex.org/W2077655061","https://openalex.org/W2083367796","https://openalex.org/W2086583481","https://openalex.org/W2088678410","https://openalex.org/W2334145331","https://openalex.org/W2336544565","https://openalex.org/W2344012311","https://openalex.org/W2903040337","https://openalex.org/W2911041448","https://openalex.org/W2918286848","https://openalex.org/W2946009010","https://openalex.org/W2985623171","https://openalex.org/W3018941397","https://openalex.org/W3035088831","https://openalex.org/W6607383429","https://openalex.org/W6631862072","https://openalex.org/W6703161458"],"related_works":["https://openalex.org/W2021099221","https://openalex.org/W2112919228","https://openalex.org/W1988318322","https://openalex.org/W105333286","https://openalex.org/W4390947848","https://openalex.org/W4323652453","https://openalex.org/W2800582356","https://openalex.org/W2106962382","https://openalex.org/W2382532955","https://openalex.org/W2074316639"],"abstract_inverted_index":{"In":[0,24],"a":[1,85],"recent":[2],"article,":[3,26],"the":[4,17,29,50,55,67,70,74,77,81,92,98],"first":[5,30,51],"and":[6,16,31,40],"second":[7,32,75],"kinds":[8,33],"of":[9,13,34,37,45,60,69,84],"multivariate":[10],"Chebyshev":[11],"polynomials":[12],"fractional":[14,38,56,82],"degree,":[15,39],"relevant":[18],"integral":[19],"repesentations,":[20],"have":[21],"been":[22],"studied.":[23],"this":[25],"we":[27,41,53],"introduce":[28],"pseudo-Lucas":[35],"functions":[36],"show":[42],"possible":[43],"applications":[44],"these":[46],"new":[47],"functions.":[48],"For":[49,73],"kind,":[52,76],"compute":[54],"Newton":[57],"sum":[58],"rules":[59],"any":[61],"orthogonal":[62],"polynomial":[63],"set":[64],"starting":[65],"from":[66],"entries":[68],"Jacobi":[71],"matrix.":[72],"representation":[78],"formulas":[79],"for":[80],"powers":[83],"r\u00d7r":[86],"matrix,":[87],"already":[88],"introduced":[89],"by":[90],"using":[91],"pseudo-Chebyshev":[93],"functions,":[94],"are":[95],"extended":[96],"to":[97],"Lucas":[99],"case.":[100]},"counts_by_year":[{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3}],"updated_date":"2026-07-23T08:03:31.855105","created_date":"2021-04-13T00:00:00"}
