Publication Date

Spring 5-22-1956

Abstract

The importance of the classical orthogonal polynomials has long been acknowledged. It has not been possible, however, to represent them in such a way that all of their important properties are immediately evident. In particular, the location of the zeros of these polynomials is of considerable interest.

This thesis is primarily concerned with a different technique in which Kamke's transformation is applied to the differential equations frequently used to define these polynomials. The resulting trigonometric differential equations cannot be explicitly solved either, but certain characteristics of these solutions facilitate the derivation of approximations to the zeroes of the solutions.

Degree Name

Mathematics

Level of Degree

Masters

Department Name

Mathematics & Statistics

First Committee Member (Chair)

C.E. Buell

Second Committee Member

J.V. Lewis

Third Committee Member

F.G. Gehry

Language

English

Keywords

Orthogonal Polynomials, Sturm's Method, Kamke's Transformation

Document Type

Thesis

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