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