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Function $n(s)$ is given implicitly as $n! = s$. How can I find an asymptotic for $n(s)$? I cannot understand, how can I make an explicit function from this to calculate an asymptotic, as there is no reverse operation for factorial (I mean, like root is reversal to pow, and so on).

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    See [here](http://mathoverflow.net/questions/12828/inverse-gamma-function).2012-10-06

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