= Two-particle distribution function
{title2=$f_2(z,z_\star,t)$}
For $N$ identical particles with symmetric, unit-normalized <phase-space distribution function> $D_N$, the number-normalized two-particle marginal is $f_2(z_1,z_2)=N(N-1)\int D_N\,dz_3\cdots dz_N$. Its integral over $z_2$ is $(N-1)f(z_1)$ and its full integral is $N(N-1)$. The factorial convention counts ordered distinct pairs and absorbs the combinatorial coefficient in the first <BBGKY hierarchy> equation. It does not imply statistical independence of the pair.
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