Sturm-Liouville eigenfunctions expressed in determinant form
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Authors
Phillips, Michael D.
Subjects
Sturm-Liouville eigenfunctions, determinant forms of
Advisors
Latta, G.E.
Date of Issue
1991-06
Date
June 1991
Publisher
Monterey, California. Naval Postgraduate School
Language
en_US
Abstract
The purpose of this thesis is to investigate and establish Sturm- Liouville properties for special eigenfunctions which are expressed in determinant form. In particular, a special case is presented where the elements of the determinant are Legendre polynomials. This type of determinant has a probability background dealing in birth and death processes. The method of analysis used in this thesis is a new approach to solving this specific example. This investigation involves systems of differential equations and Prufer's analysis in the phase plane. The following are new results obtained in addition to solving the special case mentioned above. Special determinants of hypergeometric functions also possess Sturm-Liouville properties. As a special case, a different proof of Turan's Inequality is provided. Finally, several theorems are presented for Sturm-Liouville systems of differential equations with polynomial coefficients
Type
Thesis
Description
Series/Report No
Department
Department of Mathematics
Organization
Naval Postgraduate School (U.S.)
Identifiers
NPS Report Number
Sponsors
Funder
Format
53 p.
Citation
Distribution Statement
Approved for public release; distribution is unlimited.
Rights
This publication is a work of the U.S. Government as defined in Title 17, United States Code, Section 101. Copyright protection is not available for this work in the United States.