\[\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}z}^{2}}=\left(\frac{1}{2w}+\frac{1}{w-1}%
\right)\left(\frac{\mathrm{d}w}{\mathrm{d}z}\right)^{2}-\frac{1}{z}\frac{%
\mathrm{d}w}{\mathrm{d}z}+\frac{(w-1)^{2}}{z^{2}}\left(\alpha w+\frac{\beta}{w%
}\right)+\frac{\gamma w}{z}+\frac{\delta w(w+1)}{w-1},\]