Date of Award


Degree Name

Doctor of Philosophy



First Advisor

Dr. Philip Hsieh

Second Advisor

Dr. Yousef Alavi

Third Advisor

Dr. Paul Eenigenburg

Fourth Advisor

Dr. Erik Schreiner


This work provides solid asymptotic representations, sharp error bounds and stable recurrence methods (both three term and two dimensional) for the Jacobi moments. These moments are currently used in several areas of numerical analysis (numerical integration, integral equations and boundary value problems).

A powerful representation theorem, due to H. Gingold, which uses the Jacobi moments is extended and analyzed. Applications of this theorem to multi-turning point problems and several other areas are given.

For a number of important problems in mathematical physics it is not possible to prove that the currently employed methods of solution converge, or are valid in any sense. In many such cases our methods may be shown to be uniformly convergent and numerically stable.

Access Setting

Dissertation-Open Access

Included in

Mathematics Commons