An integral representation for the product of Airy functions (Q1366352)

Here the authors obtain the following integral representation for the product of two Airy functions \[ \text{Ai}(u) \text{Ai}(v)= \frac{1}{2\pi^{3/2}} \int_0^\infty \cos\Biggl(\frac{t^3}{12}+ \frac{u+v}{2}t- \frac{(u-v)^2}{4t}+ \frac{\pi}{4}\Biggr) \frac{dt}{t} \] which generalizes some results due to \textit{W. H. Reid} [ibid. 46, 159-170 (1995; Zbl 0824.33002)]. They also mention some particular cases and applications of this result.