{"id":"https://openalex.org/W4281569554","doi":"https://doi.org/10.3390/axioms11060255","title":"On the Generalized Gaussian Fibonacci Numbers and Horadam Hybrid Numbers: A Unified Approach","display_name":"On the Generalized Gaussian Fibonacci Numbers and Horadam Hybrid Numbers: A Unified Approach","publication_year":2022,"publication_date":"2022-05-26","ids":{"openalex":"https://openalex.org/W4281569554","doi":"https://doi.org/10.3390/axioms11060255"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11060255","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11060255","pdf_url":"https://www.mdpi.com/2075-1680/11/6/255/pdf?version=1655706959","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/2075-1680/11/6/255/pdf?version=1655706959","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5012797060","display_name":"Fatih Y\u0131lmaz","orcid":"https://orcid.org/0000-0001-7873-1979"},"institutions":[{"id":"https://openalex.org/I3129222432","display_name":"Ankara Hac\u0131 Bayram Veli University","ror":"https://ror.org/05mskc574","country_code":"TR","type":"education","lineage":["https://openalex.org/I3129222432"]}],"countries":["TR"],"is_corresponding":false,"raw_author_name":"Fatih Y\u0131lmaz","raw_affiliation_strings":["Department of Mathematics, Ankara Hac\u0131 Bayram Veli University, Polatl\u0131, Ankara 06900, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Ankara Hac\u0131 Bayram Veli University, Polatl\u0131, Ankara 06900, Turkey","institution_ids":["https://openalex.org/I3129222432"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041446953","display_name":"Mustafa \u00d6zkan","orcid":"https://orcid.org/0000-0002-5883-2294"},"institutions":[{"id":"https://openalex.org/I95634034","display_name":"Gazi University","ror":"https://ror.org/054xkpr46","country_code":"TR","type":"education","lineage":["https://openalex.org/I95634034"]}],"countries":["TR"],"is_corresponding":true,"raw_author_name":"Mustafa \u00d6zkan","raw_affiliation_strings":["Department of Mathematics, Faculty of Sciences, Gazi University, Yenimahalle, Ankara 06500, Turkey"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Sciences, Gazi University, Yenimahalle, Ankara 06500, Turkey","institution_ids":["https://openalex.org/I95634034"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5041446953"],"corresponding_institution_ids":["https://openalex.org/I95634034"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.8518,"has_fulltext":true,"cited_by_count":7,"citation_normalized_percentile":{"value":0.71228782,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","issue":"6","first_page":"255","last_page":"255"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12516","display_name":"Advanced Mathematical Theories and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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":0.9617999792098999,"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/T12946","display_name":"Fractal and DNA sequence analysis","score":0.9581000208854675,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/tridiagonal-matrix","display_name":"Tridiagonal matrix","score":0.8695550560951233},{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.7762768268585205},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7613993883132935},{"id":"https://openalex.org/keywords/fibonacci-polynomials","display_name":"Fibonacci polynomials","score":0.7168014645576477},{"id":"https://openalex.org/keywords/chebyshev-polynomials","display_name":"Chebyshev polynomials","score":0.6421682238578796},{"id":"https://openalex.org/keywords/orthogonal-polynomials","display_name":"Orthogonal polynomials","score":0.499955415725708},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4860537350177765},{"id":"https://openalex.org/keywords/classical-orthogonal-polynomials","display_name":"Classical orthogonal polynomials","score":0.474984347820282},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4659956693649292},{"id":"https://openalex.org/keywords/chebyshev-filter","display_name":"Chebyshev filter","score":0.4516087472438812},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.41215255856513977},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.35318830609321594},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3386954665184021},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3237422704696655},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.3150346279144287},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.11573338508605957}],"concepts":[{"id":"https://openalex.org/C51647924","wikidata":"https://www.wikidata.org/wiki/Q1755277","display_name":"Tridiagonal matrix","level":3,"score":0.8695550560951233},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.7762768268585205},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7613993883132935},{"id":"https://openalex.org/C79117305","wikidata":"https://www.wikidata.org/wiki/Q974295","display_name":"Fibonacci polynomials","level":4,"score":0.7168014645576477},{"id":"https://openalex.org/C129785596","wikidata":"https://www.wikidata.org/wiki/Q619511","display_name":"Chebyshev polynomials","level":2,"score":0.6421682238578796},{"id":"https://openalex.org/C10628310","wikidata":"https://www.wikidata.org/wiki/Q619458","display_name":"Orthogonal polynomials","level":2,"score":0.499955415725708},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4860537350177765},{"id":"https://openalex.org/C21736991","wikidata":"https://www.wikidata.org/wiki/Q17006917","display_name":"Classical orthogonal polynomials","level":3,"score":0.474984347820282},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4659956693649292},{"id":"https://openalex.org/C21424316","wikidata":"https://www.wikidata.org/wiki/Q718621","display_name":"Chebyshev filter","level":2,"score":0.4516087472438812},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.41215255856513977},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35318830609321594},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3386954665184021},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3237422704696655},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.3150346279144287},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.11573338508605957},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","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},{"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","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/axioms11060255","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11060255","pdf_url":"https://www.mdpi.com/2075-1680/11/6/255/pdf?version=1655706959","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:f2baaa27c2704fb69da2e152ff13b2e4","is_oa":true,"landing_page_url":"https://doaj.org/article/f2baaa27c2704fb69da2e152ff13b2e4","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Axioms, Vol 11, Iss 6, p 255 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/6/255/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11060255","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 11; Issue 6; Pages: 255","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11060255","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11060255","pdf_url":"https://www.mdpi.com/2075-1680/11/6/255/pdf?version=1655706959","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":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4281569554.pdf","grobid_xml":"https://content.openalex.org/works/W4281569554.grobid-xml"},"referenced_works_count":29,"referenced_works":["https://openalex.org/W1536457675","https://openalex.org/W1997108895","https://openalex.org/W2005160213","https://openalex.org/W2007789087","https://openalex.org/W2038177835","https://openalex.org/W2188429768","https://openalex.org/W2332156326","https://openalex.org/W2396337055","https://openalex.org/W2517465526","https://openalex.org/W2804729139","https://openalex.org/W2899178189","https://openalex.org/W2912244867","https://openalex.org/W2977246615","https://openalex.org/W3015969653","https://openalex.org/W3043843149","https://openalex.org/W3150324276","https://openalex.org/W3197810406","https://openalex.org/W3213466060","https://openalex.org/W3215757527","https://openalex.org/W4205939805","https://openalex.org/W4210413596","https://openalex.org/W4403207505","https://openalex.org/W4403207977","https://openalex.org/W4407277303","https://openalex.org/W6632043600","https://openalex.org/W6687002980","https://openalex.org/W6775675943","https://openalex.org/W6872852045","https://openalex.org/W6872874359"],"related_works":["https://openalex.org/W2601873326","https://openalex.org/W2164636225","https://openalex.org/W3011914617","https://openalex.org/W2089601869","https://openalex.org/W2553814308","https://openalex.org/W2292640518","https://openalex.org/W3142826978","https://openalex.org/W2031892403","https://openalex.org/W2000813559","https://openalex.org/W2810917149"],"abstract_inverted_index":{"In":[0,13,25],"this":[1,26],"paper,":[2],"we":[3,16,28,36,48,70],"consider":[4,29,49],"an":[5],"approach":[6],"based":[7],"on":[8],"the":[9,20,40,44,62,77,81],"elementary":[10],"matrix":[11,33,41],"theory.":[12],"other":[14],"words,":[15],"take":[17],"into":[18],"account":[19],"generalized":[21],"Gaussian":[22],"Fibonacci":[23],"numbers.":[24,68],"context,":[27],"a":[30],"general":[31,64],"tridiagonal":[32,53],"family.":[34],"Then,":[35,69],"obtain":[37,71],"determinants":[38,56,73],"of":[39,52,66,76,80],"family":[42],"via":[43],"Chebyshev":[45,78],"polynomials.":[46],"Moreover,":[47],"one":[50],"type":[51],"matrix,":[54],"whose":[55],"are":[57],"Horadam":[58],"hybrid":[59,67],"polynomials,":[60],"i.e.,":[61],"most":[63],"form":[65],"its":[72],"by":[74],"means":[75],"polynomials":[79],"second":[82],"kind.":[83],"We":[84],"provided":[85],"several":[86],"illustrative":[87],"examples,":[88],"as":[89],"well.":[90]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":3},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-05-27T00:00:00"}