Publication Date

2015

Document Type

Dissertation/Thesis

First Advisor

Bowman, Douglas, 1965-

Degree Name

Ph.D. (Doctor of Philosophy)

Legacy Department

Department of Mathematical Sciences

LCSH

Mathematics; Combinatorial analysis--Research; Continued fractions--Research; q-series--Research; Number theory--Research; Geometry; Differential--Research

Abstract

This dissertation establishes an Euler-Minding type theorem for the continued fraction with numerator elements --1 and denominator elements 1 + bi, where bi is a sequence of indeterminants. This theorem is employed to derive new partition identities from Ramanujan's well-known q-continued fraction which diverges to three limit points. Continued fractions that diverge to two limits are also considered: alternating partitions studied by Andrews are shown to occur in this context, and a new proof of a result of Alladi is given.

Comments

Advisors: Douglas Bowman.||Committee members: Greg Ammar; Harris Bernard; Richard Blecksmith; Bowman Douglas.

Extent

96 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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