Self-similar summation of virial expansions

Virial expansions are the series in powers of density assumed to be small. However, the equations of state require considering finite densities for which virial expansions, as a rule, diverge. In order to extrapolate a virial expansion to the values where this expansion diverges, a novel approach for the summation of virial expansions is suggested, based on self-similar approximation theory. The method is regular and uniquely defined. It allows for the determination of physically motivated poles. The accuracy of self-similar approximants is not worse than that of the best Padé approximants with fitting parameters or of Monte Carlo simulations. The self-similar summation is based solely on virial expansions, involving no fitting parameters. In some cases, self-similar summation allows for reconstructing the sought functions exactly. The approach is illustrated by summing virial expansions for hard-disc fluids, hard-sphere fluids and systems with power-law potentials.