{"id":"https://openalex.org/W4224227276","doi":"https://doi.org/10.3390/axioms11040165","title":"On a Family of Infinite Series with Reciprocal Catalan Numbers","display_name":"On a Family of Infinite Series with Reciprocal Catalan Numbers","publication_year":2022,"publication_date":"2022-04-07","ids":{"openalex":"https://openalex.org/W4224227276","doi":"https://doi.org/10.3390/axioms11040165"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11040165","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11040165","pdf_url":"https://www.mdpi.com/2075-1680/11/4/165/pdf?version=1649311636","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/2075-1680/11/4/165/pdf?version=1649311636","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5028280395","display_name":"Kunle Adegoke","orcid":"https://orcid.org/0000-0002-3933-0459"},"institutions":[{"id":"https://openalex.org/I45711476","display_name":"Obafemi Awolowo University","ror":"https://ror.org/04snhqa82","country_code":"NG","type":"education","lineage":["https://openalex.org/I45711476"]}],"countries":["NG"],"is_corresponding":false,"raw_author_name":"Kunle Adegoke","raw_affiliation_strings":["Department of Physics and Engineering Physics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria"],"affiliations":[{"raw_affiliation_string":"Department of Physics and Engineering Physics, Obafemi Awolowo University, Ile-Ife 220005, Nigeria","institution_ids":["https://openalex.org/I45711476"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5015924206","display_name":"Robert Frontczak","orcid":"https://orcid.org/0000-0002-9373-5297"},"institutions":[{"id":"https://openalex.org/I202702066","display_name":"Landesbank Baden-W\u00fcrttemberg","ror":"https://ror.org/0208vms90","country_code":"DE","type":"other","lineage":["https://openalex.org/I202702066"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Robert Frontczak","raw_affiliation_strings":["Landesbank Baden-W\u00fcrttemberg, 70173 Stuttgart, Germany"],"affiliations":[{"raw_affiliation_string":"Landesbank Baden-W\u00fcrttemberg, 70173 Stuttgart, Germany","institution_ids":["https://openalex.org/I202702066"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5082059950","display_name":"Taras Goy","orcid":"https://orcid.org/0000-0002-6212-3095"},"institutions":[{"id":"https://openalex.org/I4210155269","display_name":"Vasyl Stefanyk Precarpathian National University","ror":"https://ror.org/0576vga12","country_code":"UA","type":"education","lineage":["https://openalex.org/I4210155269"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Taras Goy","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 76018 Ivano-Frankivsk, Ukraine"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 76018 Ivano-Frankivsk, Ukraine","institution_ids":["https://openalex.org/I4210155269"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015924206"],"corresponding_institution_ids":["https://openalex.org/I202702066"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.2499,"has_fulltext":true,"cited_by_count":2,"citation_normalized_percentile":{"value":0.48618155,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":95},"biblio":{"volume":"11","issue":"4","first_page":"165","last_page":"165"},"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":0.9998000264167786,"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/T10948","display_name":"Advanced Combinatorial Mathematics","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2607","display_name":"Discrete Mathematics and Combinatorics"},"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/catalan-number","display_name":"Catalan number","score":0.9478336572647095},{"id":"https://openalex.org/keywords/reciprocal","display_name":"Reciprocal","score":0.89357990026474},{"id":"https://openalex.org/keywords/catalan","display_name":"Catalan","score":0.8886427879333496},{"id":"https://openalex.org/keywords/fibonacci-number","display_name":"Fibonacci number","score":0.7519125938415527},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.7301512360572815},{"id":"https://openalex.org/keywords/series","display_name":"Series (stratigraphy)","score":0.6348358392715454},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4744231104850769},{"id":"https://openalex.org/keywords/recurrence-relation","display_name":"Recurrence relation","score":0.4574931561946869},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.39975374937057495},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.34176120162010193},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.32974469661712646},{"id":"https://openalex.org/keywords/linguistics","display_name":"Linguistics","score":0.0988260805606842},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.06710413098335266}],"concepts":[{"id":"https://openalex.org/C43929256","wikidata":"https://www.wikidata.org/wiki/Q270513","display_name":"Catalan number","level":2,"score":0.9478336572647095},{"id":"https://openalex.org/C2777742833","wikidata":"https://www.wikidata.org/wiki/Q1964083","display_name":"Reciprocal","level":2,"score":0.89357990026474},{"id":"https://openalex.org/C164105321","wikidata":"https://www.wikidata.org/wiki/Q7026","display_name":"Catalan","level":2,"score":0.8886427879333496},{"id":"https://openalex.org/C173734053","wikidata":"https://www.wikidata.org/wiki/Q47577","display_name":"Fibonacci number","level":2,"score":0.7519125938415527},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7301512360572815},{"id":"https://openalex.org/C143724316","wikidata":"https://www.wikidata.org/wiki/Q312468","display_name":"Series (stratigraphy)","level":2,"score":0.6348358392715454},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4744231104850769},{"id":"https://openalex.org/C201292218","wikidata":"https://www.wikidata.org/wiki/Q740970","display_name":"Recurrence relation","level":2,"score":0.4574931561946869},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.39975374937057495},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.34176120162010193},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.32974469661712646},{"id":"https://openalex.org/C41895202","wikidata":"https://www.wikidata.org/wiki/Q8162","display_name":"Linguistics","level":1,"score":0.0988260805606842},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.06710413098335266},{"id":"https://openalex.org/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C120665830","wikidata":"https://www.wikidata.org/wiki/Q14620","display_name":"Optics","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},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/axioms11040165","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11040165","pdf_url":"https://www.mdpi.com/2075-1680/11/4/165/pdf?version=1649311636","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:fa78765f942f4cff9f72d5d35b7e3018","is_oa":true,"landing_page_url":"https://doaj.org/article/fa78765f942f4cff9f72d5d35b7e3018","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 4, p 165 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/4/165/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11040165","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","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11040165","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11040165","pdf_url":"https://www.mdpi.com/2075-1680/11/4/165/pdf?version=1649311636","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/W4224227276.pdf","grobid_xml":"https://content.openalex.org/works/W4224227276.grobid-xml"},"referenced_works_count":30,"referenced_works":["https://openalex.org/W68100126","https://openalex.org/W96771674","https://openalex.org/W1567172441","https://openalex.org/W2099953837","https://openalex.org/W2503492899","https://openalex.org/W2505714894","https://openalex.org/W2620430121","https://openalex.org/W2767660854","https://openalex.org/W2886111847","https://openalex.org/W2908717431","https://openalex.org/W2909272291","https://openalex.org/W2949020075","https://openalex.org/W2995511558","https://openalex.org/W3036967620","https://openalex.org/W3037807423","https://openalex.org/W3043439746","https://openalex.org/W3045929156","https://openalex.org/W3125394761","https://openalex.org/W3131791742","https://openalex.org/W3136494114","https://openalex.org/W3152350344","https://openalex.org/W3155782876","https://openalex.org/W4230861636","https://openalex.org/W4253699484","https://openalex.org/W4288095634","https://openalex.org/W4386082396","https://openalex.org/W6748391814","https://openalex.org/W6768535601","https://openalex.org/W6781275664","https://openalex.org/W6792194519"],"related_works":["https://openalex.org/W2404725689","https://openalex.org/W1653529408","https://openalex.org/W2951311768","https://openalex.org/W4298144150","https://openalex.org/W2331795269","https://openalex.org/W2103167772","https://openalex.org/W2182556717","https://openalex.org/W1493023638","https://openalex.org/W2153986476","https://openalex.org/W2340799374"],"abstract_inverted_index":{"We":[0,12],"study":[1],"a":[2],"certain":[3],"family":[4,20,40],"of":[5,18,38,48],"infinite":[6],"series":[7],"with":[8],"reciprocal":[9],"Catalan":[10],"numbers.":[11],"first":[13],"evaluate":[14],"two":[15,46],"special":[16],"candidates":[17],"the":[19,35,39],"in":[21],"closed":[22],"form,":[23],"where":[24],"we":[25,32],"also":[26],"present":[27],"some":[28],"Catalan\u2013Fibonacci":[29],"relations.":[30],"Then,":[31],"focus":[33],"on":[34],"general":[36],"properties":[37],"and":[41],"prove":[42],"explicit":[43],"formulas,":[44],"including":[45],"types":[47],"integral":[49],"representations.":[50]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-20T23:20:44.827607","created_date":"2025-10-10T00:00:00"}