Definition:Lambert W Function/Principal Branch/Real Valued

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The principal branch of the Lambert W function is the real function $W_0: \hointr {-\dfrac 1 e} \to \to \hointr {-1} \to$ such that:

$x = \map {W_0} x e^{\map {W_0} x}$

Also denoted as

When the principal branch is the only branch under consideration, the subscript is sometimes omitted:

$x = \map W x e^{\map W x}$

Source of Name

This entry was named for Johann Heinrich Lambert.