Out of one, many-Using moment expansions of the virial relation to deduce universal density functionals from a single system

Moment expansions for density functionals are revisited. This allows for a simple proof of the equivalence between the integrodifferential virial relation and the coordinate-scaling equation. The virial relation is then used to show how, starting from an exact and explicit form of a functional for one system, one may deduce the exact functional for other systems with the same number of electrons.