Doctoral Dissertations

Keywords and Phrases

Binomial Coefficient; Eigenvalue; Factorial; Harmonic Numbers; Time Scales

Abstract

"We offer analogs to the falling factorial and rising factorial functions for the set of harmonic numbers, as well as a mixed factorial function called the M-factorial. From these concepts, we develop a harmonic analog of the binomial coefficient and an alternate expression of the harmonic exponential function and establish several identities. We generalize from the harmonic numbers to a general time scale and demonstrate how solutions to some second order eigenvalue problems and partial dynamic equations can be constructed using power series built from the M-factorial function"--Abstract, page iii.

Advisor(s)

Morgan, Ilene H.

Committee Member(s)

Clark, Stephen L.
Grow, David E.
Roe, Robert Paul
Hilgers, Michael Gene

Department(s)

Mathematics and Statistics

Degree Name

Ph. D. in Mathematics

Publisher

Missouri University of Science and Technology

Publication Date

Spring 2017

Pagination

x, 100 pages

Note about bibliography

Includes bibliographic references (pages 98-99).

Rights

© 2017 Reginald Alfred Brigham II, All rights reserved.

Document Type

Dissertation - Open Access

File Type

text

Language

English

Thesis Number

T 11078

Electronic OCLC #

992174536

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Included in

Mathematics Commons

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