  Unconventional way of handling the perturbative series is presented with the
help of Heaviside transformation with respect to the mass. We apply Heaviside
transform to the effective potential in the massive Gross-Neveu model and carry
out perturbative approximation of the massless potential by dealing with the
resulting Heaviside function. We find that accurate values of the dynamical
mass can be obtained from the Heaviside function already at finite orders where
just the several of diagrams are incorporated. We prove that our approximants
converges to the exact massless potential in the infinite order. Small mass
expansion of the effective potential can be also obtained in our approach.
