\[w_{2}(z)=(z-z_{0})^{\alpha_{2}}\sum_{\begin{subarray}{c}s=0\\
s\neq\alpha_{1}-\alpha_{2}\end{subarray}}^{\infty}b_{s}(z-z_{0})^{s}+cw_{1}(z)%
\ln\left(z-z_{0}\right),\]