Sturm-Liouville Eigenfunctions Expressed in Determinant Form

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.

Open PDF

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1991
Accession Number
ADA245991

Entities

People

  • Michael D. Phillips

Organizations

  • Naval Postgraduate School

Tags

Communities of Interest

  • Air Platforms

DTIC Thesaurus Topics

  • Algebra
  • Boundaries
  • Boundary Value Problems
  • Classification
  • Differential Equations
  • Eigenvalues
  • Eigenvectors
  • Equations
  • Hypergeometric Functions
  • Intervals
  • Mathematics
  • Orthogonality
  • Oscillation
  • Schools
  • Security
  • Sequences
  • Trajectories

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Linear Algebra