Value of Ai(0)

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Theorem

The following formula holds: $$\mathrm{Ai}(0)=\dfrac{1}{3^{\frac{2}{3}}\Gamma\left(\frac{2}{3} \right)}=0.3550280538\ldots,$$ where $\mathrm{Ai}$ denotes the Airy Ai function and $\Gamma$ denotes the gamma function.

Proof