  We calculate the second virial coefficient of anyons whose wave function does
not vanish at coincidence points. This kind of anyons appear naturally when one
generalizes the hard-core boundary condition according to self-adjoint
extension method in quantum mechanics, and also when anyons are treated field
theoretically by applying renormalization procedure to nonrelativistic
Chern-Simons field theory. For the anyons which do not satisfy hard-core
boundary condition, it is argued that the other scale-invariant limit is more
relevant in high-temperature limit where virial expansion is useful.
Furthermore, the cusp existing at the bosonic point for hard-core anyons
disappears in all the other cases; instead it is shown that a new cusp is
generated at the fermionic point. A physical explanation is given.
