Perturbative ground state energy of three anyons in a harmonic potential

We calculate the ground state energy of three anyons in a harmonic potential near fermionic statistics. The energy is given by E0(α)=ω[4+1.300α2+O(α3)], where 4ω is the ground state energy of three fermions. We compare this with the energy of the exact eigenstate that interpolates to the ground state at α=1 (bosonic statistics). There is a cross-over between ground states at α=0.3 where the two results coincide