  The available virial coefficients for the 2D hard disks model are transformed
into a matrix representation of the thermodynamic potentials, which allows for
an accurate description of the whole fluid phase, up to the phase transition.
We find that the fluid phase terminates at the transition point, supporting the
Kosterlitz-Thouless-Halperin-Nelson-Young picture of a second order phase
transition into a Hexatic phase. The density and pressure at the transition are
calculated from the available first ten virial coefficients, and are found to
be in excellent agreement with recent Monte-Carlo calculations. Finally, we
calculate the equation of state in the critical region.
