Publication Date

2021

Document Type

Dissertation/Thesis

First Advisor

Bowman, Douglas

Degree Name

M.S. (Master of Science)

Legacy Department

Department of Mathematical Sciences

Abstract

One of the most famous results from q-series is that of the Rogers-Ramanujan continued fraction, given by [special characters omitted]. G.E. Andrews and D. Bowman gave a full extension of this continued fraction using G.N. Watson’s nonterminating very well-poised 8φ7 function. As opposed to Ramanujan’s generalization that only used four variables, this generalization is given in seven variables, and certain q-series identities naturally arise from it. As a special case of their theorem, Andrews and Bowman gave the following identity: [special characters omitted]. This thesis will give a full proof of Andrews and Bowman’s result, as well as investigate other special cases of their continued fraction that have not been discovered before. Many identities will be verified using an open-source symbolic algebra package called Maxima.

Extent

65 pages

Language

eng

Publisher

Northern Illinois University

Rights Statement

In Copyright

Rights Statement 2

NIU theses are protected by copyright. They may be viewed from Huskie Commons for any purpose, but reproduction or distribution in any format is prohibited without the written permission of the authors.

Media Type

Text

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Mathematics Commons

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