\[\Psi_{2}\left(0,y\right)=\begin{cases}\sqrt{\ifrac{\pi}{y}}\left(\exp\left(%
\tfrac{1}{4}i\pi\right)+o\left(1\right)\right),&y\to+\infty,\\
\sqrt{\ifrac{\pi}{|y|}}\exp\left(-\tfrac{1}{4}i\pi\right)\left(1+i\sqrt{2}\exp%
\left(-\frac{1}{4}iy^{2}\right)+o\left(1\right)\right),&y\to-\infty.\end{cases}\]