What is the inverse function of the Log Gamma function?

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What is the inverse function of the Log Gamma function?

$\log\Gamma(x)$

http://mathworld.wolfram.com/LogGammaFunction.html

Can it be inverted, and why not, if not?

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Consider:

$$\log(\Gamma(x))=y$$

Then, solving for $x$, we get:

$$x=\Gamma^{-1}(e^y)$$

And then this is where you put in a formula for the inverse of the gamma function.