\[S(\epsilon,r)=\begin{cases}2\cos\left(\pi|\epsilon|^{-1/2}\right),&\epsilon<0,%
r>0,\\
0,&\epsilon<0,r<0,\\
e^{\pi\epsilon^{-1/2}},&\epsilon>0,r>0,\\
e^{-\pi\epsilon^{-1/2}},&\epsilon>0,r<0.\end{cases}\]