Let $z \in D$. Show that the function $\Psi : t \mapsto ( 1 - t z ) e ^ { L ( t z ) }$ is constant on $[ 0,1 ]$, and deduce that $$\exp ( L ( z ) ) = \frac { 1 } { 1 - z }$$
Let $z \in D$. Show that the function $\Psi : t \mapsto ( 1 - t z ) e ^ { L ( t z ) }$ is constant on $[ 0,1 ]$, and deduce that
$$\exp ( L ( z ) ) = \frac { 1 } { 1 - z }$$