\[\operatorname{arcsinh}z=z-\frac{1}{2}\frac{z^{3}}{3}+\frac{1\cdot 3}{2\cdot 4}%
\frac{z^{5}}{5}-\frac{1\cdot 3\cdot 5}{2\cdot 4\cdot 6}\frac{z^{7}}{7}+\cdots,\]