This project centers around an analysis of the algebraic properties of the solutions of linear differential equations with polynomial coefficients and the development of algorithms based upon this analysis that can be used to construct improved interpolation schemes. In particular, the principal investigator will use the theory of galois groups to solve linear differential equations in terms of special functions. He will study also the algebraic structure of these special functions with a view to improving algorithms for integration of the differential equation in finite terms. And finally he will employ techniques from the algebraic theory of differential equations to develop improved interpolation formulas for sparse polynomials and rational functions.
