Bridge function

The bridge functions are infinite series of irreducible diagrams $D_{i}$ :

B^{(2)} (r) = ρ^{2} \frac{1}{2} D_{1} (r) + ρ^{3} [D_{2} (r) + D_{3} (r)] + ρ^{4} [. . .] + . . .

and

B^{(1)} (r) = \frac{1}{3} B^{(2)} (r) + ρ^{3} [\frac{1}{6} D_{2} (r) - \frac{1}{12} D_{3} (r)] + ρ^{4} [. . .] + . . .

where $ρ$ is the density of the fluid.

Universality of the Bridge functional

For Rosenfeld's principle of the universality of the bridge functional see Ref. 2.