How to represent factorial as a product notation?

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Original question: Is there any way to write $x!$ as a Pi notation? $$x!=\prod\text{?}$$

The answer should have been obvious $$x!=\prod_{r=1}^xr$$

Now I have an additional question:

Is it possible to write $\left(2(\ x+1 )\ \right)!$ as a product notation? $$(2(x+1))!=\prod?$$

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3 Answers

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You can write like this:
$$x!=\prod_{r=1}^x\text{r}$$

For additional question:

$$(2x+2)!=\prod_{r=1}^{(2x+2)}\text{r}$$

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It is possible. We have definition of n! as product (r), running from 1 to n. I hope you asked for this pardon otherwise.

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For a non-integer number,

$n!=\prod_{k=1}^{\infty}\left( \frac{k+1}{k}\right)^{n}\frac{k}{n+k}.$

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