# 3.5.1.3.51 lambertW

## Definition:

The lambertW(x[, branch, offset]) function calculates an approximate value for the real branches of Lambert’s W function (sometimes known as the ‘product log’ or ‘Omega’ function), which is the inverse function of

$f\left ( w \right )=we^{w}$ for $w \in C$

The function f is many-to-one, and so, except at 0, W is multivalued.

This labtalk function is implemented from NAG9(c05bac), you may refer to detailed information in the NAG library.

## Parameters:

x

The value if offset is not chosen, or the offset $\Delta x$ from $-exp\left ( -1 \right )$ of the intended argument to W if the offset is chosen.

branch

Optional. The real branch required, should be 0 or -1.

offset

Optional. Controls whether or not x is being specified as an offset from $-exp\left ( -1 \right )$, should be 0 or 1.

## Examples:

lambertW(0.25)=0.203888

lambertW(0.5, 0, 0) = 0.351734

lambertW(0.75, 0, 1) = 0.286834

lambertW(-0.25, -1, 0) = -2.153292