{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/72779"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/72779","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues","abstract":"Some of the most interesting of Ramanujan's continued fraction identities are those involving ratios of Gamma functions in Chapter 12 of his second notebook. This thesis develops a method for deriving such identities, using hypergeometric functions as the main tool. We begin by deriving a continued fraction identity, use it to prove Ramanujan's Entry 34, and then use the method to obtain new identities and relate them to two of Ramanujan's identities. We next prove Ramanujan's Entries 36 and 39. 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Finally, we rework the method for use with basic hypergeometric functions and use it to find q-analogues of the earlier new results.","abstract_has_math":false,"creators":["Reuter, Victoria"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Berndt, Bruce C.","Reznick, Bruce","Hildebrand, A.J.","Stolarsky, Kenneth B."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-21T19:48:06Z","date_published":"2015-01-21T19:48:06Z","updated_at":"2026-07-22T22:26:07Z","subjects":["hypergeometric functions","continued fractions","gamma function","basic hypergeometric functions","q-analogue","q-series","Ramanujan","Ramanujan's notebooks"],"languages":["en"],"rights":["Copyright 2014 Victoria Jane Reuter"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/72779","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Berndt, Bruce C.","Reznick, Bruce","Hildebrand, A.J.","Stolarsky, Kenneth B."]},{"key":"dc:creator","label":"Author","values":["Reuter, Victoria"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-01-21T19:48:06Z","2014-12","2015-01-21"]},{"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":["hypergeometric functions","continued fractions","gamma function","basic hypergeometric functions","q-analogue","q-series","Ramanujan","Ramanujan's notebooks"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2014 Victoria Jane Reuter"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/72779"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Some of the most interesting of Ramanujan's continued fraction identities are those involving ratios of Gamma functions in Chapter 12 of his second notebook. 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