Author

Sarah Wesley

Publication Date

2018

Document Type

Dissertation/Thesis

First Advisor

Bowman, Douglas, 1965-

Degree Name

Ph.D. (Doctor of Philosophy)

Department

Department of Mathematical Sciences

LCSH

Mathematics

Abstract

This dissertation studies the method of iteration introduced by Nathan J. Fine for the function [Special characters omitted], where q is a fixed complex number with |q| < 1, |t| < 1 and (z)[sub n] = (1 - z)(1 - zq)(1 - zq²)...(1 - zq^(n-1)) for n < 0 and (z)₀ = 1 (for z [element of] C). Generalizing Fine's methods yields new basic hypergeometric identities. Certain identities have partition theory interpretations and are proved combinatorially using the method of overpartitions. Among other basic hypergeometric identities, generalizations of the Rogers-Fine identity are given.

Comments

Advisors: Douglas Bowman.||Committee members: Daniel Grubb; Nathan Krislock; Jeffrey Thunder.||Includes illustrations.||Includes bibliographical references.

Extent

177 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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