Definition:Product of Differences

Definition
Let $n \in \Z, n > 0$ be an integer.

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

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. The Product of Differences as a polynomial in $x$ over a field $F$ of degree $n$ is by definition the Vandermonde Polynomial.