\begin{definition}[Definition:Falling Factorial]
Let $x$ be a real number (but usually an integer).
Let $n$ be a positive integer.
Then '''$x$ to the (power of) $n$ falling''' is:
:$\ds x^{\underline n} := \prod_{j \mathop = 0}^{n - 1} \paren {x - j} = x \paren {x - 1} \cdots \paren {x - n + 1}$
\end{definition}