Definition:Product of Differences

Definition
Let $n \in \Z_{>0}$ be a strictly positive integer.

Then $\Delta_n \left({x_1, x_2, \ldots, x_n}\right)$ is defined as:
 * $\displaystyle \Delta_n = \prod_{1 \mathop \le i \mathop < j \mathop \le n} \left({x_i - x_j}\right)$

Thus $\Delta_n$ is the product of the difference of all pairs of $\left\{{x_1, x_2, \ldots, x_n}\right\}$ where the index of the first is less than the index of the second.

Also see

 * Definition:Vandermonde Polynomial