Perhaps it is a stupid question, but I would like to know how to calculate
$\left(\frac{1}{n}\right)!$
I know $n! = n\cdot(n-1)\cdot(n-2)\cdots1$ and...?
$$\left(\frac{1}{n}\right)!$$
2026-04-01 13:48:44.1775051324
How can I calculate $(\frac{1}{n})!$
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In general there isn't any nice closed form for $\left(\frac{1}{n}\right)!$, apart from $\left(\frac{1}{2}\right)! = \frac{1}{2}\sqrt{\pi}$ and the trivial $1!=1$. However, if $n\in\{3,4,6,12,24\}$ we have that $\left(\frac{1}{n}\right)!$ has a closed form in terms of elliptic integrals of the first kind, hence it can be computed really fast through the AGM mean. By recalling that $\left(\frac{1}{n}\right)!=\Gamma\left(1+\frac{1}{n}\right)$, have a look at this Wikipedia page.