$\Gamma(x)$ is said to have a minimum around $x_0\approx 1.46$. Is it known that $x_0$ is an irrational number? A transcendental number for that matter? Can $x_0$ be expressed in terms of more familiar constants, like $e$ or $\pi$ ? What kind of number is $x_0$ exactly? Information on these questions seems curiously scarce even in the internet.
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4Does this answer your question? Minimum of the Gamma Function $\Gamma (x)$ for $x\gt;0$. How to find $x_{\min}$? – John B May 24 '23 at 22:41
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@John B Not really... – ashpool May 26 '23 at 00:25