Definition:Falling Factorial

Definition
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:
 * $\ds x^{\underline n} := \prod_{j \mathop = 0}^{n - 1} \paren {x - j} = x \paren {x - 1} \cdots \paren {x - n + 1}$

Also known as
This is referred to as the $n$th falling factorial power of $x$.

It can also be referred to as the $n$th falling factorial of $x$.

Also see

 * Definition:Rising Factorial
 * Definition:Factorial
 * Definition:Gamma Function


 * Properties of Falling Factorial