Asymptotic representations for some functions and integrals connected with the Airy function

A. I. Nikishov, V. I. Ritus

The asymptotic representations of the functions ${\mathrm{Ai}}_1(x),\mathrm{Gi}(x),{\mathrm{Ai}}^{\prime }(x),{\mathrm{Ai}}^2(x),{\mathrm{Bi}}^2(x)$ are obtained. As a by-product, the factorial identity (21'…