{"id":"https://openalex.org/W3152347718","doi":"https://doi.org/10.3390/sym13040534","title":"An Analysis of the Recurrence Coefficients for Symmetric Sobolev-Type Orthogonal Polynomials","display_name":"An Analysis of the Recurrence Coefficients for Symmetric Sobolev-Type Orthogonal Polynomials","publication_year":2021,"publication_date":"2021-03-25","ids":{"openalex":"https://openalex.org/W3152347718","doi":"https://doi.org/10.3390/sym13040534","mag":"3152347718"},"language":"en","primary_location":{"id":"doi:10.3390/sym13040534","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040534","pdf_url":"https://www.mdpi.com/2073-8994/13/4/534/pdf?version=1616660180","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/13/4/534/pdf?version=1616660180","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5032845386","display_name":"Lino G. Garza","orcid":"https://orcid.org/0000-0002-2755-0235"},"institutions":[{"id":"https://openalex.org/I894135719","display_name":"University of Monterrey","ror":"https://ror.org/02arnxw97","country_code":"MX","type":"education","lineage":["https://openalex.org/I894135719"]},{"id":"https://openalex.org/I916541031","display_name":"Universidad de Colima","ror":"https://ror.org/04znxe670","country_code":"MX","type":"education","lineage":["https://openalex.org/I916541031"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Lino G. Garza","raw_affiliation_strings":["Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Monterrey, San Pedro Garza Garc\u00eda, Nuevo Le\u00f3n 66238, Mexico","Facultad de Ciencias, Universidad de Colima, Colima 28045, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-2755-0235","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Monterrey, San Pedro Garza Garc\u00eda, Nuevo Le\u00f3n 66238, Mexico","institution_ids":["https://openalex.org/I894135719"]},{"raw_affiliation_string":"Facultad de Ciencias, Universidad de Colima, Colima 28045, Mexico","institution_ids":["https://openalex.org/I916541031"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5014651000","display_name":"Luis E. Garza","orcid":"https://orcid.org/0000-0002-2569-186X"},"institutions":[{"id":"https://openalex.org/I894135719","display_name":"University of Monterrey","ror":"https://ror.org/02arnxw97","country_code":"MX","type":"education","lineage":["https://openalex.org/I894135719"]},{"id":"https://openalex.org/I916541031","display_name":"Universidad de Colima","ror":"https://ror.org/04znxe670","country_code":"MX","type":"education","lineage":["https://openalex.org/I916541031"]}],"countries":["MX"],"is_corresponding":false,"raw_author_name":"Luis E. Garza","raw_affiliation_strings":["Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Monterrey, San Pedro Garza Garc\u00eda, Nuevo Le\u00f3n 66238, Mexico","Facultad de Ciencias, Universidad de Colima, Colima 28045, Mexico"],"raw_orcid":"https://orcid.org/0000-0002-2569-186X","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Monterrey, San Pedro Garza Garc\u00eda, Nuevo Le\u00f3n 66238, Mexico","institution_ids":["https://openalex.org/I894135719"]},{"raw_affiliation_string":"Facultad de Ciencias, Universidad de Colima, Colima 28045, Mexico","institution_ids":["https://openalex.org/I916541031"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051633177","display_name":"Edmundo J. Huertas","orcid":"https://orcid.org/0000-0001-6802-3303"},"institutions":[{"id":"https://openalex.org/I189268942","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78","country_code":"ES","type":"education","lineage":["https://openalex.org/I189268942"]}],"countries":["ES"],"is_corresponding":true,"raw_author_name":"Edmundo J. Huertas","raw_affiliation_strings":["Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, Ctra. Madrid-Barcelona, Km. 33,600, Facultad de Ciencias, 28805 Alcal\u00e1 de Henares, Madrid, Spain"],"raw_orcid":"https://orcid.org/0000-0001-6802-3303","affiliations":[{"raw_affiliation_string":"Departamento de F\u00edsica y Matem\u00e1ticas, Universidad de Alcal\u00e1, Ctra. Madrid-Barcelona, Km. 33,600, Facultad de Ciencias, 28805 Alcal\u00e1 de Henares, Madrid, Spain","institution_ids":["https://openalex.org/I189268942"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5051633177"],"corresponding_institution_ids":["https://openalex.org/I189268942"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.08370321,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":"4","first_page":"534","last_page":"534"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11191","display_name":"Mathematical functions and polynomials","score":0.9997000098228455,"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/T11191","display_name":"Mathematical functions and polynomials","score":0.9997000098228455,"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/T12589","display_name":"Differential Equations and Boundary Problems","score":0.9815999865531921,"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9733999967575073,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/recurrence-relation","display_name":"Recurrence relation","score":0.8429946899414062},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.788874626159668},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.6511371731758118},{"id":"https://openalex.org/keywords/type","display_name":"Type (biology)","score":0.6126627922058105},{"id":"https://openalex.org/keywords/sobolev-space","display_name":"Sobolev space","score":0.5376438498497009},{"id":"https://openalex.org/keywords/measure","display_name":"Measure (data warehouse)","score":0.5240026712417603},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.5112655162811279},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.5089206695556641},{"id":"https://openalex.org/keywords/product","display_name":"Product (mathematics)","score":0.47059309482574463},{"id":"https://openalex.org/keywords/term","display_name":"Term (time)","score":0.4626392424106598},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.4528660178184509},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.4336183965206146},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35498446226119995},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.333565354347229},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.08522617816925049},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.0559614896774292}],"concepts":[{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.8429946899414062},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.788874626159668},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.6511371731758118},{"id":"https://openalex.org/C2777299769","wikidata":"https://www.wikidata.org/wiki/Q3707858","display_name":"Type (biology)","level":2,"score":0.6126627922058105},{"id":"https://openalex.org/C99730327","wikidata":"https://www.wikidata.org/wiki/Q1501536","display_name":"Sobolev space","level":2,"score":0.5376438498497009},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5240026712417603},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.5112655162811279},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.5089206695556641},{"id":"https://openalex.org/C90673727","wikidata":"https://www.wikidata.org/wiki/Q901718","display_name":"Product (mathematics)","level":2,"score":0.47059309482574463},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.4626392424106598},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.4528660178184509},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.4336183965206146},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35498446226119995},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.333565354347229},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08522617816925049},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0559614896774292},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.0},{"id":"https://openalex.org/C77088390","wikidata":"https://www.wikidata.org/wiki/Q8513","display_name":"Database","level":1,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","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}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/sym13040534","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040534","pdf_url":"https://www.mdpi.com/2073-8994/13/4/534/pdf?version=1616660180","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:0738d205a684418bbab1bed76cbd4283","is_oa":true,"landing_page_url":"https://doaj.org/article/0738d205a684418bbab1bed76cbd4283","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":"Symmetry, Vol 13, Iss 4, p 534 (2021)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2073-8994/13/4/534/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/sym13040534","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":"Symmetry","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/sym13040534","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym13040534","pdf_url":"https://www.mdpi.com/2073-8994/13/4/534/pdf?version=1616660180","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"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":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G8522214838","display_name":null,"funder_award_id":"CM/JIN/2019-010","funder_id":"https://openalex.org/F4320323755","funder_display_name":"Universidad de Alcal\u00e1"}],"funders":[{"id":"https://openalex.org/F4320323755","display_name":"Universidad de Alcal\u00e1","ror":"https://ror.org/04pmn0e78"}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W3152347718.pdf"},"referenced_works_count":27,"referenced_works":["https://openalex.org/W126109759","https://openalex.org/W143770817","https://openalex.org/W1978280564","https://openalex.org/W1988502665","https://openalex.org/W1994029617","https://openalex.org/W2003935003","https://openalex.org/W2021467799","https://openalex.org/W2024472793","https://openalex.org/W2079891462","https://openalex.org/W2083781733","https://openalex.org/W2112552845","https://openalex.org/W2137247574","https://openalex.org/W2167717375","https://openalex.org/W2264315341","https://openalex.org/W2473897877","https://openalex.org/W2573432118","https://openalex.org/W2626080132","https://openalex.org/W2760145570","https://openalex.org/W2771903190","https://openalex.org/W2963587004","https://openalex.org/W2980671223","https://openalex.org/W3005845648","https://openalex.org/W3099608462","https://openalex.org/W3121984935","https://openalex.org/W4214609664","https://openalex.org/W4249126432","https://openalex.org/W6732178933"],"related_works":["https://openalex.org/W936279937","https://openalex.org/W80861483","https://openalex.org/W3104921728","https://openalex.org/W2085028572","https://openalex.org/W4300493934","https://openalex.org/W4302480035","https://openalex.org/W2952111850","https://openalex.org/W1491565486","https://openalex.org/W2951709720","https://openalex.org/W4298331257"],"abstract_inverted_index":{"In":[0],"this":[1],"contribution":[2],"we":[3,60],"obtain":[4],"some":[5],"algebraic":[6],"properties":[7,67],"associated":[8],"with":[9,15,49],"the":[10,18,69,81],"sequence":[11],"of":[12],"polynomials":[13],"orthogonal":[14],"respect":[16],"to":[17,64],"Sobolev-type":[19],"inner":[20],"product:p,qs=\u222bRp(x)q(x)d\u03bc(x)+M0p(0)q(0)+M1p\u2032(0)q\u2032(0),":[21],"where":[22],"p,q":[23],"are":[24,28],"polynomials,":[25],"M0,":[26],"M1":[27],"non-negative":[29],"real":[30],"numbers":[31],"and":[32,52,72],"\u03bc":[33],"is":[34],"a":[35,41,45,73],"symmetric":[36],"positive":[37],"measure.":[38],"These":[39],"include":[40],"five-term":[42],"recurrence":[43,47,70],"relation,":[44],"three-term":[46],"relation":[48],"rational":[50],"coefficients,":[51],"an":[53],"explicit":[54],"expression":[55],"for":[56,68],"its":[57],"norms.":[58],"Moreover,":[59],"use":[61],"these":[62],"results":[63],"deduce":[65],"asymptotic":[66],"coefficients":[71],"nonlinear":[74],"difference":[75],"equation":[76],"that":[77],"they":[78],"satisfy,":[79],"in":[80],"particular":[82],"case":[83],"when":[84],"d\u03bc(x)=e\u2212x4dx.":[85]},"counts_by_year":[],"updated_date":"2026-05-22T06:13:13.366637","created_date":"2025-10-10T00:00:00"}
