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Description
Title: | Hypergeometric functions, continued fractions for products of gamma functions, and q-analogues |
Author(s): | Reuter, Victoria |
Director of Research: | Berndt, Bruce C. |
Doctoral Committee Chair(s): | Reznick, Bruce |
Doctoral Committee Member(s): | Berndt, Bruce C.; Hildebrand, A.J.; Stolarsky, Kenneth B. |
Department / Program: | Mathematics |
Discipline: | Mathematics |
Degree Granting Institution: | University of Illinois at Urbana-Champaign |
Degree: | Ph.D. |
Genre: | Dissertation |
Subject(s): | hypergeometric functions
continued fractions gamma function basic hypergeometric functions q-analogue q-series Ramanujan Ramanujan's notebooks |
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. Finally, we rework the method for use with basic hypergeometric functions and use it to find q-analogues of the earlier new results. |
Issue Date: | 2015-01-21 |
URI: | http://hdl.handle.net/2142/72779 |
Rights Information: | Copyright 2014 Victoria Jane Reuter |
Date Available in IDEALS: | 2015-01-21 |
Date Deposited: | 2014-12 |
This item appears in the following Collection(s)
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Dissertations and Theses - Mathematics
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Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois