Convergence of the virial expansion for the classical canonical ensemble

The infinite set of coupled integral equations for correlation functions in the case of classical canonical ensemble similar to those of Kirkwood–Salsburg is derived starting with the Bogoliubov integral-differential equations. The theorem of existence and uniqueness of solution is proved for such equations by the method of a non-linear operator ones in the Banach space. The solution has a form of the power series in density.