Comparison between equations-of-motion and green's function methods for the particle-hole response function

We show that, apart from a few differences, the equations-of-motion method of McKoy et al. provides the leading correction to the random phase approximation (with exchange) in the fully renormalized response function (density-density correlation function). Thus, their equations-of-motion method is shown to be equivalent to a partial summation of infinite sets of terms in the perturbation expansion of the response function.