Generalization of Euler's summation formula to path integrals

A recently developed analytical method for systematic improvement of the convergence of path integrals is used to derive a generalization of Euler's summation formula for path integrals. The first p terms in this formula improve convergence of path integrals to the continuum limit from 1/N to 1/Np, where N is the coarseness of the discretization. Monte Carlo simulations performed on several different models show that the analytically derived speedup holds.