{"id":"https://openalex.org/W4293009441","doi":"https://doi.org/10.3390/axioms11090426","title":"Approximation for the Ratios of the Confluent Hypergeometric Function \u03a6D(N) by the Branched Continued Fractions","display_name":"Approximation for the Ratios of the Confluent Hypergeometric Function \u03a6D(N) by the Branched Continued Fractions","publication_year":2022,"publication_date":"2022-08-24","ids":{"openalex":"https://openalex.org/W4293009441","doi":"https://doi.org/10.3390/axioms11090426"},"language":"en","primary_location":{"id":"doi:10.3390/axioms11090426","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090426","pdf_url":null,"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://doi.org/10.3390/axioms11090426","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5053674517","display_name":"\u0422. \u041c. Antonova","orcid":"https://orcid.org/0000-0002-0358-4641"},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Tamara Antonova","raw_affiliation_strings":["Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Stepana Bandera Str., 79013 Lviv, Ukraine"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Stepana Bandera Str., 79013 Lviv, Ukraine","institution_ids":["https://openalex.org/I98435010"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5060979027","display_name":"Roman Dmytryshyn","orcid":"https://orcid.org/0000-0003-2845-0137"},"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":true,"raw_author_name":"Roman Dmytryshyn","raw_affiliation_strings":["Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, Ukraine"],"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, Ukraine","institution_ids":["https://openalex.org/I4210155269"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066282658","display_name":"\u0420. \u0420. \u041a\u0443\u0440\u043a\u0430","orcid":"https://orcid.org/0000-0003-3057-1413"},"institutions":[{"id":"https://openalex.org/I98435010","display_name":"Lviv Polytechnic National University","ror":"https://ror.org/0542q3127","country_code":"UA","type":"education","lineage":["https://openalex.org/I98435010"]}],"countries":["UA"],"is_corresponding":false,"raw_author_name":"Roman Kurka","raw_affiliation_strings":["Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Stepana Bandera Str., 79013 Lviv, Ukraine"],"affiliations":[{"raw_affiliation_string":"Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Stepana Bandera Str., 79013 Lviv, Ukraine","institution_ids":["https://openalex.org/I98435010"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5060979027"],"corresponding_institution_ids":["https://openalex.org/I4210155269"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":3.8673,"has_fulltext":false,"cited_by_count":11,"citation_normalized_percentile":{"value":0.94408209,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"11","issue":"9","first_page":"426","last_page":"426"},"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/T12404","display_name":"Mathematical Approximation and Integration","score":0.9911999702453613,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/T12661","display_name":"Iterative Methods for Nonlinear Equations","score":0.9901999831199646,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"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/hypergeometric-function","display_name":"Hypergeometric function","score":0.7519949674606323},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.6560634970664978},{"id":"https://openalex.org/keywords/confluent-hypergeometric-function","display_name":"Confluent hypergeometric function","score":0.5716028809547424},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5610830783843994},{"id":"https://openalex.org/keywords/branching","display_name":"Branching (polymer chemistry)","score":0.5600709915161133},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.4659031331539154},{"id":"https://openalex.org/keywords/generalized-hypergeometric-function","display_name":"Generalized hypergeometric function","score":0.4581105411052704},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.43750664591789246},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.4342457354068756},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.42331695556640625},{"id":"https://openalex.org/keywords/chemistry","display_name":"Chemistry","score":0.18452182412147522},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.06392031908035278}],"concepts":[{"id":"https://openalex.org/C197320386","wikidata":"https://www.wikidata.org/wiki/Q21028472","display_name":"Hypergeometric function","level":2,"score":0.7519949674606323},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6560634970664978},{"id":"https://openalex.org/C148160416","wikidata":"https://www.wikidata.org/wiki/Q783948","display_name":"Confluent hypergeometric function","level":3,"score":0.5716028809547424},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5610830783843994},{"id":"https://openalex.org/C206175624","wikidata":"https://www.wikidata.org/wiki/Q595731","display_name":"Branching (polymer chemistry)","level":2,"score":0.5600709915161133},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.4659031331539154},{"id":"https://openalex.org/C158241908","wikidata":"https://www.wikidata.org/wiki/Q109744257","display_name":"Generalized hypergeometric function","level":3,"score":0.4581105411052704},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.43750664591789246},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.4342457354068756},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.42331695556640625},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.18452182412147522},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.06392031908035278},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","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/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C178790620","wikidata":"https://www.wikidata.org/wiki/Q11351","display_name":"Organic chemistry","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/axioms11090426","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090426","pdf_url":null,"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:ace7b400d2ac4b1bafc8b50e779af723","is_oa":true,"landing_page_url":"https://doaj.org/article/ace7b400d2ac4b1bafc8b50e779af723","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 9, p 426 (2022)","raw_type":"article"},{"id":"pmh:oai:mdpi.com:/2075-1680/11/9/426/","is_oa":true,"landing_page_url":"https://dx.doi.org/10.3390/axioms11090426","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 9; Pages: 426","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.3390/axioms11090426","is_oa":true,"landing_page_url":"https://doi.org/10.3390/axioms11090426","pdf_url":null,"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":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":18,"referenced_works":["https://openalex.org/W209808057","https://openalex.org/W217327495","https://openalex.org/W1996680223","https://openalex.org/W2008501278","https://openalex.org/W2045306405","https://openalex.org/W2049855857","https://openalex.org/W2093148814","https://openalex.org/W2922311782","https://openalex.org/W2955078300","https://openalex.org/W2983107807","https://openalex.org/W3007250564","https://openalex.org/W3092264301","https://openalex.org/W3119672848","https://openalex.org/W3155294098","https://openalex.org/W3216118242","https://openalex.org/W3216594270","https://openalex.org/W3217111580","https://openalex.org/W4200324982"],"related_works":["https://openalex.org/W3192609840","https://openalex.org/W2090151112","https://openalex.org/W2010866598","https://openalex.org/W2905308183","https://openalex.org/W4246122464","https://openalex.org/W3098293399","https://openalex.org/W4289106892","https://openalex.org/W1977217926","https://openalex.org/W2997127250","https://openalex.org/W3126885930"],"abstract_inverted_index":{"The":[0,42,65],"paper":[1],"deals":[2],"with":[3,30,82],"the":[4,9,12,21,27,37,98,106],"problem":[5],"of":[6,8,11,16,26,33,39,44,49,67,105,109,115],"expansion":[7],"ratios":[10,54,108],"confluent":[13,50],"hypergeometric":[14,51],"function":[15,52,110],"N":[17,31],"variables":[18],"\u03a6D(N)(a,b\u00af;c;z\u00af)":[19,111],"into":[20],"branched":[22],"continued":[23],"fractions":[24],"(BCF)":[25],"general":[28],"form":[29],"branches":[32],"branching":[34],"and":[35,71,86],"investigates":[36],"convergence":[38,77],"these":[40,94],"BCF.":[41],"algorithms":[43],"construction":[45],"for":[46,62,79],"BCF":[47,81,95],"expansions":[48],"\u03a6D(N)":[53],"are":[55,88,101],"based":[56],"on":[57],"some":[58,113],"given":[59],"recurrence":[60],"relations":[61],"this":[63],"function.":[64],"case":[66],"nonnegative":[68],"parameters":[69],"a,b1,\u2026,bN\u22121":[70],"positive":[72],"c":[73],"is":[74,91],"considered.":[75],"Some":[76],"criteria":[78],"obtained":[80],"elements":[83],"in":[84,112],"RN":[85],"CN":[87],"established.":[89],"It":[90],"proven":[92],"that":[93],"converge":[96],"to":[97],"functions":[99],"which":[100],"an":[102],"analytic":[103],"continuation":[104],"above-mentioned":[107],"domain":[114],"CN.":[116]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":2},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2022-08-25T00:00:00"}
