Abstract
It is shown that the equation of state of fluid systems can be expanded around non-null densities if the well known virial series is generalized by considering its coefficients as density dependent. This in turn leads to a hierarchy of differential equations that describe the coefficients bj (ρ). Starting from the already known equation of state for hard bodies in d = 0,1,2,3 dimensions this hierarchy is analysed and the behaviour of both the reducible bj (ρ) and irreducible β∼ j (ρ) cluster integrals is discussed. New virial coefficients bj (ρ) have been introduced with a simpler density dependence. Their asymptotic (j → ∞) behaviour is discussed.