{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86801"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86801","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the Convergence and Divergence of Q-Continued Fractions on and Off the Unit Circle","abstract":"\"General convergence is a concept introduced by Lisa Lorentzen (nee Jacobson) and is stronger in the sense that classical convergence implies general convergence. We show that all continued fractions in a certain class, which includes the Rogers-Ramanujan continued fractions and the three \"\"Ramanujan-Selberg\"\" continued fractions, diverge in the general sense at an uncountable set of points on the unit circle. We also show that the Rogers-Ramanujan continued fraction converges generally at all roots of unity (in contrast to classical convergence) and that it does not converge generally at any point outside the unit circle.\"","abstract_html":""General convergence is a concept introduced by Lisa Lorentzen (nee Jacobson) and is stronger in the sense that classical convergence implies general convergence. We show that all continued fractions in a certain class, which includes the Rogers-Ramanujan continued fractions and the three ""Ramanujan-Selberg"" continued fractions, diverge in the general sense at an uncountable set of points on the unit circle. We also show that the Rogers-Ramanujan continued fraction converges generally at all roots of unity (in contrast to classical convergence) and that it does not converge generally at any point outside the unit circle."","abstract_has_math":false,"creators":["Mc Laughlin, James"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Douglas Bowman"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T15:19:36Z","date_published":"2015-09-28T15:19:36Z","updated_at":"2026-07-22T22:26:27Z","subjects":["Mathematics"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3070383"],"render_values":[{"text":"(MiAaPQ)AAI3070383","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/86801","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Douglas Bowman"]},{"key":"dc:creator","label":"Author","values":["Mc Laughlin, James"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T15:19:36Z","10000-01-01","2002"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/86801","(MiAaPQ)AAI3070383"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["\"General convergence is a concept introduced by Lisa Lorentzen (nee Jacobson) and is stronger in the sense that classical convergence implies general convergence. We show that all continued fractions in a certain class, which includes the Rogers-Ramanujan continued fractions and the three \"\"Ramanujan-Selberg\"\" continued fractions, diverge in the general sense at an uncountable set of points on the unit circle. We also show that the Rogers-Ramanujan continued fraction converges generally at all roots of unity (in contrast to classical convergence) and that it does not converge generally at any point outside the unit circle.\"","Made available in DSpace on 2015-09-28T15:19:36Z (GMT). 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We show that all continued fractions in a certain class, which includes the Rogers-Ramanujan continued fractions and the three \"\"Ramanujan-Selberg\"\" continued fractions, diverge in the general sense at an uncountable set of points on the unit circle. We also show that the Rogers-Ramanujan continued fraction converges generally at all roots of unity (in contrast to classical convergence) and that it does not converge generally at any point outside the unit circle.\"","Made available in DSpace on 2015-09-28T15:19:36Z (GMT). No. of bitstreams: 2 license.txt: 4848 bytes, checksum: 96035ab3f5e1c23cc7138a224ce498bd (MD5) 3070383.pdf: 3172983 bytes, checksum: 5cc62de209148f4680002f69a4c4048b (MD5) Previous issue date: 2002","Embargo set by: Seth Robbins for item 88082 Lift date: Forever Reason: Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","Restricted to the U of I community idenfinitely during batch ingest of legacy ETDs","U of I Only","91 p.","Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2002."],"dc:identifier":["http://hdl.handle.net/2142/86801","(MiAaPQ)AAI3070383"],"dc:language":["eng"],"dc:subject":["Mathematics"],"dc:title":["On the Convergence and Divergence of Q-Continued Fractions on and Off the Unit Circle"],"dc:type":["text"],"thesis:degree_discipline":["Mathematics"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:26:27Z"}