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 $\Gamma(-1)=0!=1$.
2026-03-26 22:12:58.1774563178
What function does Wolfram Alpha plot instead of the factorial?
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It is a plot of $\Gamma(x+1)$, known to equal $x!$ at integers.