  It has been shown that the large--scale correlation functions of the density
field (and velocity divergence field) follow a specific hierarchy in the
quasilinear regime and for Gaussian initial conditions (Bernardeau 1992). The
exact relationships between the cumulants of the probability distribution
functions (the so-called $S_p$ parameters) are however sensitive to the
smoothing window function applied to the fields. In this paper, I present a
method to derive the whole series of the $S_p$ parameters when the density
field is smoothed with a top--hat window function. The results are valid for
any power spectrum and any cosmological parameters. Similar calculations are
presented for the velocity divergence field.
  The resulting shapes of the one--point probability distribution functions of
the cosmic density and the velocity divergence fields are given as a function
of the power spectrum and $\Omega$. Simple analytical fits are proposed when
the index of the power spectrum is -1. Comparisons with numerical simulations
prove these analytical results to be extremely accurate.
