The Analytic Approach to Recursion Relations

Solution of algebraic recursion relations in the most obvious fashion may produce unwieldy expressions. If the structure of the recursion is well understood, a better method may be to calculate the coefficient of each term in the answer by analysis of all ways in which that term can be generated by the reeursion relation. This technique has been applied with great success to the WKB (phase-integral) approximation for ordinary differential equations and systems. In progress is a more difficult application, to differential geometry and relativity (Synge-DeWitt tensors).