We determine approximate formula for the ground state energy of anyons in 2D
parabolic well which is valid for the arbitrary anyonic factor \nu and number
of particles N in the system. We assume that centre of mass motion energy is
not excluded from the energy of the system. Formula for ground state energy
calculated by variational principle contains logarithmic divergence at small
distances between two anyons which is regularized by cut-off parameter. By
equating this variational formula to the analogous formula of Wu near bosonic
limit (\nu ~ 0)we determine the value of the cut-off and thus derive the
approximate formula for the ground state energy for the any \nu and N. We
checked this formula at \nu=1, when anyons become fermions, for the systems
containing two to thirty particles. We find that our approximate formula has an
accuracy within 6%. It turns out, at the big number N limit the ground state
energy has square root dependence on factor \nu.Comment: 7 page