Definition:Lambert W Function/Lower Branch

Definition
The lower branch of the Lambert W function is the real function $W_{-1}: \hointr {-\dfrac 1 e} 0 \to \hointl \gets {-1}$ such that:


 * $x = \map {W_{-1} } x e^{\map {W_{-1} } x}$

Linguistic Note
Though this branch has a generally accepted notation, $W_{-1}$, it doesn't seem to have an accepted name in the literature.