Equivalence of two approaches for the inhomogeneous density in the canonical ensemble

In this Brief Report we show that the inhomogeneous density obtained from a density-functional theory of classical fluids in the canonical ensemble (CE), recently presented by White et al. [Phys. Rev. Lett. 84, 1220 (2000)], is equivalent to first order to the result of the series expansion of the CE inhomogeneous density introduced by Gonzalez et al. [Phys. Rev. Lett. 79, 2466 (1997)].