In fact, for this special case every n-particle density is independent of coordinates, and can be computed explicitly ρ ρ ( n ) ( r 1 , … … , r n ) = N ! ( N − − n ) ! 1 V N ∏ ∏ i = n + 1 N ∫ ∫ d 3 r i 1 = N ! ( N − − n ) ! 1 V n For N ≫ ≫ n , the non-interacting n-particle density is approximately ρ ρ non-interacting ( n ) ( r 1 , … … , r N ) = ( 1 − − n ( n − − 1 ) / 2 N + ⋯ ⋯ ) ρ ρ n ≈ ≈ ρ ρ n . With this in hand, the n-point correlation function g ( n ) is defined by factoring out the non-interacting contribution, ρ ρ ( n ) ( r 1 , … … , r n ) = ρ ρ non-interacting ( n ) g ( n ) ( r 1 … … , r n ) Explicitly, this definition reads g ( n ) ( r 1 , … … , r n ) = V N N ! ( ∏ ∏ i = n + 1 N 1 V ∫ ∫ d 3 r i ) 1 Z N ∑ ∑ π π ∈ ∈ S N e − − β β U ( r π π ( 1 ) , … … , r π π ( N ) ) where it is clear that the n-point correlation function is dimensionless.