Definition:Lambert W Function/Lower Branch

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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:

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


Source of Name

This entry was named for Johann Heinrich Lambert.


Linguistic Note

The term lower branch (of the Lambert $W$ function) was invented by $\mathsf{Pr} \infty \mathsf{fWiki}$.

As such, it is not generally expected to be seen in this context outside $\mathsf{Pr} \infty \mathsf{fWiki}$.

Though this branch has a generally accepted notation, $W_{-1}$, it does not seem to have a standard name in the literature.