convert/Airy converts, when possible, special functions admitting a 1F1 or 0F1 hypergeometric representation into Airy functions. The Airy functions are

FunctionAdvisor( Airy );

The 2 functions in the "Airy" class are:

$\left[\mathrm{AiryAi}\,\mathrm{AiryBi}\right]$

$\mathrm{BesselK}\left(\frac{1}{3}\,z\right)$

$\mathrm{BesselK}\left(\frac{1}{3}\,z\right)$

$\mathrm{convert}\left(\,\mathrm{Airy}\right)$

$\mathrm{\pi }\sqrt{\frac{3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{2}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{z^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}\mathrm{AiryAi}\left(\frac{3^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{2}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{z}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{2}\right)$

$\mathrm{BesselJ}\left(\frac{1}{3}\,z\right)$

$\mathrm{BesselJ}\left(\frac{1}{3}\,z\right)$

$\mathrm{convert}\left(\,\mathrm{Airy}\right)$

$\frac{\sqrt{\frac{3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{2}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{z^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}\left(\sqrt{3}\mathrm{AiryAi}\left(-\frac{3^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{2}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{z}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{2}\right)-\mathrm{AiryBi}\left(-\frac{3^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{2}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{z}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{2}\right)\right)}{2}$

$\mathrm{BesselI}\left(-\frac{1}{3}\,\frac{2}{3}{z}^{\frac{3}{2}}\right)$

$\mathrm{BesselI}\left(-\frac{1}{3}\,\frac{2z^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}{3}\right)$

$\mathrm{convert}\left(\,\mathrm{Airy}\right)$

$\frac{\sqrt{3}\left(\sqrt{3}\mathrm{AiryAi}\left({\left(z^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)+\mathrm{AiryBi}\left({\left(z^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)\right)}{2{\left(z^{\raisebox{1ex}{$3$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}$

$\mathrm{KummerM}\left(\frac{5}{6}\,\frac{5}{3}\,2\mathrm{I}z\right)$

$\mathrm{KummerM}\left(\frac{5}{6}\,\frac{5}{3}\,2\mathrm{I}z\right)$

$\mathrm{convert}\left(\,\mathrm{Airy}\right)$

$\frac{{\ⅇ}^{\mathrm{I}z}\mathrm{\pi }\sqrt{3}{2}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\sqrt{\frac{3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{2}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{z^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}\left(\sqrt{3}\mathrm{AiryAi}\left(-\frac{3^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{2}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{z}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{2}\right)-\mathrm{AiryBi}\left(-\frac{3^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{2}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{z}^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{2}\right)\right)}{9\mathrm{\Gamma }\left(\frac{2}{3}\right)z^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}$

$\mathrm{MeijerG}\left(\left[\left[\right]\,\left[\frac{1}{6}\,\frac{2}{3}\right]\right]\,\left[\left[\frac{1}{3}\,0\right]\,\left[\frac{2}{3}\,\frac{1}{6}\right]\right]\,z\right)$

$\mathrm{MeijerG}\left(\left[\left[\right]\,\left[\frac{1}{6}\,\frac{2}{3}\right]\right]\,\left[\left[\frac{1}{3}\,0\right]\,\left[\frac{2}{3}\,\frac{1}{6}\right]\right]\,z\right)$

$\mathrm{convert}\left(\,\mathrm{Airy}\right)$

$\frac{\sqrt{\frac{3^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}{{\left(-z\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}}}\left(\sqrt{3}\left(z^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+{\left(-z\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)\mathrm{AiryAi}\left(-3^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\left(-z\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)+\left(-z^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}+{\left(-z\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)\mathrm{AiryBi}\left(-3^{\raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}{\left(-z\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}\right)\right)}{4{\left(-z\right)}^{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}\mathrm{\pi }}$