\[\int_{0}^{\infty}e^{-pt}\operatorname{Ai}\left(t\right)\,\mathrm{d}t=e^{-p^{3}%
/3}\left(\frac{1}{3}-\frac{p{{}_{1}F_{1}}\left(\tfrac{1}{3};\tfrac{4}{3};%
\tfrac{1}{3}p^{3}\right)}{3^{4/3}\Gamma\left(\tfrac{4}{3}\right)}+\frac{p^{2}{%
{}_{1}F_{1}}\left(\tfrac{2}{3};\tfrac{5}{3};\tfrac{1}{3}p^{3}\right)}{3^{5/3}%
\Gamma\left(\tfrac{5}{3}\right)}\right),\]