\[\operatorname{arctan}z=\frac{z}{z^{2}+1}\*\left(1+\frac{2}{3}\frac{z^{2}}{1+z^%
{2}}+\frac{2\cdot 4}{3\cdot 5}\left(\frac{z^{2}}{1+z^{2}}\right)^{2}+\cdots%
\right),\]