\[z(\rho,\phi)=2\pi\left(\rho^{-1/3}u(\phi)\cos\left(\rho\widetilde{f}(\phi)%
\right)\operatorname{Ai}\left(-\rho^{2/3}\Delta(\phi)\right)\*(1+O\left(1/\rho%
\right))+\rho^{-2/3}v(\phi)\sin\left(\rho\widetilde{f}(\phi)\right)%
\operatorname{Ai}'\left(-\rho^{2/3}\Delta(\phi)\right)\*(1+O\left(1/\rho\right%
))\right),\]