Guggenheim Equation for a System of Hard Spheres and Its Generalization

In the present work, for the first time, a generalized Guggenheim equation for a system of hard spheres has been obtained based on the use of Euler's accelerated convergence method. This equation allows for the consideration of an arbitrary number of known virial coefficients. For the metastable region, this equation is generalized to account for the asymptotic behaviour of free energy at high densities. The obtained expression for the compressibility of the homogeneous phase of a hard sphere system describes the data of the numerical experiment within the limits of its accuracy.