LambertW¶

LambertW(x, principal=True)¶

Lambert W function.

The Lambert W function $\mathrm{W}(x)$ is defined by the relation:

$x = \mathrm{W}(x) \exp(\mathrm{W}(x))$

Parameters:

Returns:

resultfloat

If principal is True : $result = \mathrm{W}_0(x)$ . $\mathrm{W}_0(x)$ is referred to as the principal branch of the Lambert W function. It denotes the upper part of the function whose domain is $[-1/e, +\infty[$ and range $[-1, +\infty[$ .
If principal is False : $result = \mathrm{W}_{-1}(x)$ . $\mathrm{W}_{-1}(x)$ is the second real branch of the Lambert W function. It denotes the lower part of the function whose domain is $[-1/e, 0[$ and range $]-\infty, -1]$ .

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