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Look to the second graph where Wolfram Alpha gives a continuous factorial function:

What is the second graph?

It is not the gamma function, since that has $\Gamma(-1)=0!=1$.

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It is a plot of $\Gamma(x+1)$, known to equal $x!$ at integers.

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  • $\begingroup$ Oh, of course! Thank you. $\endgroup$ – wythagoras Jun 13 '15 at 14:46

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