\[(z\sigma^{\prime\prime}-\sigma^{\prime})^{2}+2(\sigma^{\prime})^{2}(z\sigma^{%
\prime}-2\sigma)-4\kappa_{0}\kappa_{\infty}(\theta+1)\theta_{\infty}z\sigma^{%
\prime}=4\kappa_{0}^{2}\kappa_{\infty}^{2}z^{2}.\]