{"id":"https://openalex.org/W2169841346","doi":"https://doi.org/10.1285/i15900932v33n2p35","title":"On some continued fraction expansions for the ratios of the function","display_name":"On some continued fraction expansions for the ratios of the function","publication_year":2013,"publication_date":"2013-01-01","ids":{"openalex":"https://openalex.org/W2169841346","doi":"https://doi.org/10.1285/i15900932v33n2p35","mag":"2169841346"},"language":"en","primary_location":{"id":"pmh:oai:ese-journals.unisalento.it:article/13737","doi":null,"is_oa":true,"landing_page_url":"https://ese-journals.unisalento.it/index.php/notemat/article/view/13737","pdf_url":"https://ese-journals.unisalento.it/index.php/notemat/article/download/13737/12118","source":{"id":"https://openalex.org/S4306521020","display_name":"Note di matematica/Note di matematica - Universit\u00e0 degli studi di Lecce","issn_l":"1123-2536","issn":["1123-2536","1590-0932"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["ddh","doaj","dongbi-c","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310317549","host_organization_name":"University of Salento","host_organization_lineage":["https://openalex.org/P4310317549"],"host_organization_lineage_names":["University of Salento"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1123-2536","raw_type":"info:eu-repo/semantics/article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"diamond","oa_url":"https://ese-journals.unisalento.it/index.php/notemat/article/download/13737/12118","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041266399","display_name":"D. D. Somashekara","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Somashekara, D.D.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5037936343","display_name":"S. Shalini","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shalini, S.L.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5113857772","display_name":"Konappa Narasimha Murthy","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Narasimha Murthy, K.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.0,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"33","issue":"2","first_page":"35","last_page":"42"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":1.0,"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"}},"topics":[{"id":"https://openalex.org/T11428","display_name":"Advanced Mathematical Identities","score":1.0,"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/T11191","display_name":"Mathematical functions and polynomials","score":9.999999747378752e-05,"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/T11166","display_name":"Analytic Number Theory Research","score":0.0,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/continued-fraction-expansion","display_name":"continued fraction expansion","score":0.7609999775886536},{"id":"https://openalex.org/keywords/ramanujan-s-lost-notebook","display_name":"Ramanujan's lost notebook","score":0.9330000281333923}],"concepts":[{"id":"https://openalex.org/C131220774","wikidata":"https://www.wikidata.org/wiki/Q1441456","display_name":"Ramanujan's sum","level":2,"score":0.8328914046287537},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.7226042747497559},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6926450133323669},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5828347206115723},{"id":"https://openalex.org/C169903001","wikidata":"https://www.wikidata.org/wiki/Q3264987","display_name":"Reciprocity (cultural anthropology)","level":2,"score":0.4905223250389099},{"id":"https://openalex.org/C127808406","wikidata":"https://www.wikidata.org/wiki/Q3535240","display_name":"Ramanujan tau function","level":3,"score":0.4743463099002838},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44229114055633545},{"id":"https://openalex.org/C20080352","wikidata":"https://www.wikidata.org/wiki/Q206816","display_name":"Continued fraction","level":3,"score":0.43718841671943665},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.07758137583732605},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.060506582260131836},{"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/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},{"id":"https://openalex.org/C77805123","wikidata":"https://www.wikidata.org/wiki/Q161272","display_name":"Social psychology","level":1,"score":0.0},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.0},{"id":"https://openalex.org/C39613435","wikidata":"https://www.wikidata.org/wiki/Q846677","display_name":"Remainder","level":2,"score":0.0}],"mesh":[],"locations_count":5,"locations":[{"id":"pmh:oai:ese-journals.unisalento.it:article/13737","doi":null,"is_oa":true,"landing_page_url":"https://ese-journals.unisalento.it/index.php/notemat/article/view/13737","pdf_url":"https://ese-journals.unisalento.it/index.php/notemat/article/download/13737/12118","source":{"id":"https://openalex.org/S4306521020","display_name":"Note di matematica/Note di matematica - Universit\u00e0 degli studi di Lecce","issn_l":"1123-2536","issn":["1123-2536","1590-0932"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["ddh","doaj","dongbi-c","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310317549","host_organization_name":"University of Salento","host_organization_lineage":["https://openalex.org/P4310317549"],"host_organization_lineage_names":["University of Salento"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1123-2536","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:eprints.uni-mysore.ac.in:9675","doi":null,"is_oa":false,"landing_page_url":"http://eprints.uni-mysore.ac.in/9675/1/Mat_2013_Somashekara.pdf","pdf_url":"http://eprints.uni-mysore.ac.in/9675/1/Mat_2013_Somashekara.pdf","source":{"id":"https://openalex.org/S4306400737","display_name":"MyPrints@UOM (Mysore University Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I204743663","host_organization_name":"University of Mysore","host_organization_lineage":["https://openalex.org/I204743663"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"acceptedVersion","is_accepted":true,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:siba-ese.unisalento.it:article/13737","doi":null,"is_oa":true,"landing_page_url":"http://siba-ese.unisalento.it/index.php/notemat/article/view/13737","pdf_url":null,"source":{"id":"https://openalex.org/S7407050994","display_name":"Universit\u00e0 del Salento","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I142910587","host_organization_name":"University of Salento","host_organization_lineage":["https://openalex.org/I142910587"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Note di Matematica; Volume 33, Issue 2 (2013); 35-42","raw_type":"Article Journal"},{"id":"doi:10.1285/i15900932v33n2p35","doi":"https://doi.org/10.1285/i15900932v33n2p35","is_oa":true,"landing_page_url":"https://doi.org/10.1285/i15900932v33n2p35","pdf_url":null,"source":{"id":"https://openalex.org/S7407050994","display_name":"Universit\u00e0 del Salento","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I142910587","host_organization_name":"University of Salento","host_organization_lineage":["https://openalex.org/I142910587"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Dataset"},{"id":"mag:2169841346","doi":null,"is_oa":true,"landing_page_url":"http://siba-ese.unile.it/index.php/notemat/article/view/13737/0","pdf_url":null,"source":{"id":"https://openalex.org/S4306521020","display_name":"Note di matematica/Note di matematica - Universit\u00e0 degli studi di Lecce","issn_l":"1123-2536","issn":["1123-2536","1590-0932"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["ddh","doaj","dongbi-c","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310317549","host_organization_name":"University of Salento","host_organization_lineage":["https://openalex.org/P4310317549"],"host_organization_lineage_names":["University of Salento"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Note di matematica/Note di matematica - Universit\u00e0 degli studi di Lecce","raw_type":null}],"best_oa_location":{"id":"pmh:oai:ese-journals.unisalento.it:article/13737","doi":null,"is_oa":true,"landing_page_url":"https://ese-journals.unisalento.it/index.php/notemat/article/view/13737","pdf_url":"https://ese-journals.unisalento.it/index.php/notemat/article/download/13737/12118","source":{"id":"https://openalex.org/S4306521020","display_name":"Note di matematica/Note di matematica - Universit\u00e0 degli studi di Lecce","issn_l":"1123-2536","issn":["1123-2536","1590-0932"],"is_oa":true,"is_in_doaj":true,"is_core":false,"listed_in":["ddh","doaj","dongbi-c","norway-1","poland-20","russia-white-list-3"],"host_organization":"https://openalex.org/P4310317549","host_organization_name":"University of Salento","host_organization_lineage":["https://openalex.org/P4310317549"],"host_organization_lineage_names":["University of Salento"],"type":"journal"},"license":"cc-by-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"1123-2536","raw_type":"info:eu-repo/semantics/article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1843734400","display_name":null,"funder_award_id":"F1-17.1/","funder_id":"https://openalex.org/F4320320767","funder_display_name":"University Grants Commission"},{"id":"https://openalex.org/G4812233187","display_name":null,"funder_award_id":"F1-17.1/2011-12","funder_id":"https://openalex.org/F4320320767","funder_display_name":"University Grants Commission"},{"id":"https://openalex.org/G6036548507","display_name":null,"funder_award_id":"2011-12","funder_id":"https://openalex.org/F4320320767","funder_display_name":"University Grants Commission"},{"id":"https://openalex.org/G6267115271","display_name":null,"funder_award_id":"DRS-1","funder_id":"https://openalex.org/F4320320767","funder_display_name":"University Grants Commission"}],"funders":[{"id":"https://openalex.org/F4320320767","display_name":"University Grants Commission","ror":"https://ror.org/04p800546"}],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2169841346.pdf","grobid_xml":"https://content.openalex.org/works/W2169841346.grobid-xml"},"referenced_works_count":11,"referenced_works":["https://openalex.org/W28961898","https://openalex.org/W187428917","https://openalex.org/W630770018","https://openalex.org/W1489262469","https://openalex.org/W1561532180","https://openalex.org/W1970347768","https://openalex.org/W2012324805","https://openalex.org/W2019394773","https://openalex.org/W2019703048","https://openalex.org/W2032542008","https://openalex.org/W2087326315"],"related_works":["https://openalex.org/W7043305484","https://openalex.org/W7216764252","https://openalex.org/W2087326315","https://openalex.org/W2899436907","https://openalex.org/W2141952432","https://openalex.org/W2022582561","https://openalex.org/W2090677138","https://openalex.org/W1629483650","https://openalex.org/W2041178455","https://openalex.org/W187428917"],"abstract_inverted_index":{"In":[0,18],"his":[1],"lost":[2],"notebook,":[3],"Ramanujan":[4],"has":[5,10],"defined":[6],"a":[7,12],"function":[8],"and":[9],"given":[11],"beautiful":[13],"reciprocity":[14],"theorem":[15],"involving":[16],"$\\rho(a,~b)$.":[17],"this":[19],"paper":[20],"we":[21],"obtain":[22,40],"some":[23,33,41],"continued":[24,47,55],"fraction":[25,48,56],"expansions":[26,49],"for":[27],"the":[28,54],"ratios":[29],"of":[30,34,45],"$\\rho(a,~b)$":[31],"with":[32],"its":[35],"contiguous":[36],"functions.":[37],"We":[38],"also":[39],"interesting":[42],"special":[43],"cases":[44],"our":[46],"which":[50],"are":[51],"analogous":[52],"to":[53],"identities":[57],"stated":[58],"by":[59],"Ramanujan.\\end":[60]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2016-06-24T00:00:00"}