  The statistical distribution function of anyon is used to find the eighth
viral coefficient in the high-temperature limit and the equation of state in
the low-temperature limit. The perturbative results indicate that the
thermodynamic quantities, $Q(\alpha)$, of the free anyon gas may be factorized
in the terms characteristic of the ideal Bose ($\alpha =0$) and fermion
($\alpha =1$) gases, i.e., $Q(\alpha) = \alpha Q(1) + (1-\alpha) Q(0)$. It is
shown that the factorizable property of the thermodynamic quantities, to all
orders, can be established from the property of the equivalence between the
anyon statistics and statistics in a system with boson-fermion transmutation,
which was found by us in a recent paper (hep-th/0308095; Phys. Rev. E 51 (1995)
3729)
