  A general density-functional formalism using an extended variable-space is
presented for classical fluids in the canonical ensemble (CE). An exact
equation is derived that plays the role of the Ornstein-Zernike (OZ) equation
in the grand canonical ensemble (GCE). When applied to the ideal gas we obtain
the exact result for the total correlation function h_N. For a homogeneous
fluid with N particles the new equation only differs from OZ by 1/N and it
allows to obtain an approximate expression for h_N in terms of its GCE
counterpart that agrees with the expansion of h_N in powers of 1/N.
