  We consider a weakly-interacting Bose-Einstein condensate that rotates in
either a harmonic, or a weakly-anharmonic trapping potential. Performing
numerical calculations, we investigate the behaviour of the gas in these two
cases as the angular momentum, or equivalently as the rotational frequency of
the trap increases. While in the case of a purely-harmonic potential the gas
makes a transition from the mean-field regime to the correlated, "Laughlin",
regime, in the case of anharmonic confinement the mean-field approximation
remains always valid. We compare our derived results in these two cases, using
both the mean-field approximation, as well as the diagonalization of the
many-body Hamiltonian considering a small atom number.
