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.
Level of Degree
Mathematics & Statistics
First Committee Member (Chair)
Second Committee Member
Third Committee Member
Orthogonal Polynomials, Sturm's Method, Kamke's Transformation
Daniels, Robert L.. "The Use of Kamke's Transformation in Approximating the Zeros of Orthogonal Polynomials." (1956). https://digitalrepository.unm.edu/math_etds/88