  The pressure of a gas of particles with a uniformly repulsive pair
interaction in a finite container is shown to satisfy (exactly as a formal
object) a "viscous" Hamilton-Jacobi (H-J) equation whose solution in power
series is recursively given by the variation of constants formula. We
investigate the solution of the H-J and of its Legendre transform equation by
the Cauchy-Majorant method and provide a lower bound to the radius of
convergence on the virial series of the gas which goes beyond the threshold
established by Lagrange's inversion formula. A comparison between the behavior
of the Mayer and virial coefficients for different regimes of repulsion
intensity is also provided.
