Transformation theory of symmetric differential expressions

Abstract

We consider the problem of transforming a symmetric differential expression of even or odd order with both real and complex coefficients with a Kummer-Liouville transformation. An existence proof is given which yields an algorithm for computing exactly the coefficients of the transformed equation. By using the concept of a modified Kummer-Liouville transformation we derive explicit expressions for the coefficients of the transformed equation which are correct modulo Levinson terms only. However, the application of Levinson's theorem to asymptotic integration shows that Levinson terms have no effect on the asymptotics of the eigenfunctions.