\[\Psi_{3}\left(0,0,z\right)=\frac{\Gamma\left(\tfrac{1}{3}\right)}{|z|^{1/3}%
\sqrt{3}}+\begin{cases}o\left(1\right),&z\to+\infty,\\
\dfrac{2\sqrt{\pi}5^{1/4}}{(3|z|)^{3/4}}\left(\cos\left(\dfrac{2}{3}\left(%
\dfrac{3|z|}{5}\right)^{5/2}-\dfrac{1}{4}\pi\right)+o\left(1\right)\right),&z%
\to-\infty.\end{cases}\]