Euler Summation Formula for Path Integrals

We present and comment on some details of a new analytical method (1, 2) for systematic improvement of the convergence of path integrals of a generic N-fold discretized theory. The new methods represents a Euler summation formula for path integrals. Keeping the first p terms in this formula improves convergence of path integrals to the continuum limit to 1=Np. We have given explicit calculations up to p = 9. We have also checked this derived speedup in convergence by performing Monte Carlo simulations on several dierent models.