The Gamma function achieves a local minimum at $x^* \approx 1.46163$, where $\Gamma(x^*) \approx 0.88560$.
Can $x^*$ and $\Gamma(x^*)$ easily be proven irrational? Are they transcendental?
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1Possibly related (about the minimum of the gamma function, not about irrationality): http://math.stackexchange.com/questions/3245/ – Watson Jun 05 '16 at 12:30
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These are open problems, and not easy. – John M Jun 09 '16 at 13:07
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2@JohnM: Can you cite a source? – Lynn Jun 09 '16 at 13:15