Show that $| L ( z ) | \leq - \ln ( 1 - | z | )$ for all $z$ in $D$. Deduce that the series $\sum _ { n \geq 1 } L \left( z ^ { n } \right)$ is convergent for all $z$ in $D$.
Show that $| L ( z ) | \leq - \ln ( 1 - | z | )$ for all $z$ in $D$.\\
Deduce that the series $\sum _ { n \geq 1 } L \left( z ^ { n } \right)$ is convergent for all $z$ in $D$.