\[\ln\left(w^{(\lambda)}(\cos\theta;a,b)\right)=\begin{cases}-2\pi(a+b)\theta^{-%
1}+(2\lambda-1)\ln\left(a+b\right)+\lambda\ln 4+2(a+b)+O\left(\theta\right),&%
\theta\to 0+,\\
2\pi(b-a)\left(\pi-\theta\right)^{-1}+(2\lambda-1)\ln\left(a-b\right)+\lambda%
\ln 4+2(a-b)+O\left(\pi-\theta\right),&\theta\to\pi-,\end{cases}\]