\[\int_{0}^{\infty}t^{\alpha-1}{\operatorname{Ai}}^{2}\left(t\right)\,\mathrm{d}%
t=\frac{2\Gamma\left(\alpha\right)}{\pi^{1/2}12^{(2\alpha+5)/6}\Gamma\left(%
\frac{1}{3}\alpha+\frac{5}{6}\right)},\]