3.5.2.4.4 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
the real branch required, should be 0 or -1.
offset
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