\[\Psi^{(\mathrm{E})}\left(0,0,z\right)=\overline{\Psi^{(\mathrm{E})}\left(0,0,-%
z\right)}\\
=2\pi\sqrt{\frac{\pi z}{27}}\exp\left(\frac{2}{27}iz^{3}\right)\*\left(J_{-1/6%
}\left(\frac{2}{27}z^{3}\right)+iJ_{1/6}\left(\frac{2}{27}z^{3}\right)\right),\]