Category:Falling Factorials

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This category contains results about Falling Factorials.


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:

$\displaystyle x^{\underline n} := \prod_{j \mathop = 0}^{n - 1} \left({x - j}\right) = x \left({x - 1}\right) \cdots \left({x - n + 1}\right)$

Also see