# Definition:Lambert W Function/Principal Branch/Real Valued

## Definition

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.