{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/86947"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/86947","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"On the Rogers-Ramanujan and Ramanujan-Gollnitz-Gordon Continued Fractions","abstract":"In a manuscript of Ramanujan, published with his Lost Notebook, there are forty identities involving the Rogers-Ramanujan functions. According to G. N. Watson, the beauty of these identities is comparable to that of the Rogers-Ramanujan identities. In the final chapter, we establish modular relations involving the Gollnitz-Gordon functions which are analogous to Ramanujan's forty identities. Furthermore, we extract interesting theorems on partitions from some of the modular relations.","abstract_html":"In a manuscript of Ramanujan, published with his Lost Notebook, there are forty identities involving the Rogers-Ramanujan functions. According to G. N. Watson, the beauty of these identities is comparable to that of the Rogers-Ramanujan identities. In the final chapter, we establish modular relations involving the Gollnitz-Gordon functions which are analogous to Ramanujan&#x27;s forty identities. 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