On the Rogers-Ramanujan and Ramanujan-Gollnitz-Gordon Continued Fractions
Huang, Sen-Shan
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https://hdl.handle.net/2142/86947
Description
Title
On the Rogers-Ramanujan and Ramanujan-Gollnitz-Gordon Continued Fractions
Author(s)
Huang, Sen-Shan
Issue Date
1997
Doctoral Committee Chair(s)
Bruce, Berndt
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
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.
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