\begin{definition}[Definition:Lambert W Function/Lower Branch]
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:
:$x = \map {W_{-1} } x e^{\map {W_{-1} } x}$
{{NamedforDef|Johann Heinrich Lambert}}
\end{definition}