WKB methods for difference equations II

Summary

In a previous paper [1] it was shown how to develop solutions to difference equations analogous to WKB solutions to differential equations. In the work now reported a much more general “comparison equation” theory [2] is developed for difference equations, exploiting the fact that a difference equation can be considered as a differential equation of infinite order. Second order difference equations are considered in the main; by applying the theory to first order difference equations a useful generalization of the Euler-Maclaurin summation formula is found.