Analytic representation for the equation of state in classical statistical mechanics

For the system of classical particles interacting by pair short-range forces the explicitly convergent expansions on usual and complementary density and the contour integral representations are constructed for the all-round compression modulus, the modulus being sufficient to describe all the thermodynamic properties and being tentatively single-valued in the vicinity of the phase transition point. With the help of those the analytic representations of the equation of state as well as specific configuration integral are found. The elaborated technique is approved on the exactly solved model – the theory of the Van der Waals substance being a model “substance” for which the Van der Waals equation is the exact equation of state.