${E^{\prime}}\left(k\right)=\begin{cases}E\left(k^{\prime}\right),&|%
\operatorname{ph}k|\leq\tfrac{1}{2}\pi,\\
E\left(k^{\prime}\right)\mp 2\mathrm{i}(K\left(-k\right)-E\left(-k\right)),&%
\tfrac{1}{2}\pi<\pm\operatorname{ph}k<\pi.\end{cases}$