Abstract Schumaker This proposal is to support the ninth international conference on Approximation Theory and Related Topics in Nashville, January 3-6. These meeting have been the main general international conferences on approximation theory for the last 25 years. The objective of the conference is to provide a triennial forum for researchers in the field to discuss current work. It also will provide a forum for the awarding of the Second Vasil A. Popov Prize in Approximation Theory. There meeting will feature 7 one-hour survey lectures in addition to the one-hour lecture by the winner of the Popov Prize. Approximation is the defining feature of mathematical analysis. Compact expressions of solutions of problems arising in the physical universe rarely occur. More often, the solutions must be approximated by known quantities which have desirable properties and are easily computed. This research contributes to the dual goals of understanding the special functions of analysis and discovering their approximation properties.