Definition:Lambert W Function/Lower Branch/Linguistic Note
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Linguistic Note on Lower Branch of Lambert W Function
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.