I know that this is valid for every $s$ in the half plane $\{s:\operatorname{Re}(s)>0\}$, but does the formula extend along with the analytic continuation of the $\Gamma$ function?
2026-03-25 06:21:43.1774419703
Is $\Gamma(s+1)=s\Gamma(s)$ valid for every $s\in\mathbb{C}\setminus\{0,-1,-2,-3,\ldots\}$?
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