LambertW | omega function | product log function | W-function

The Lambert W-function, also called the omega function, is the inverse function of f(W) = W e^W. The plot above shows the function along the real axis. The principal value of the Lambert W-function is implemented in the Wolfram Language as ProductLog[z]. Different branches of the function are available in the Wolfram Language as ProductLog[k, z], where k is any integer and k = 0 corresponds to the principal value. Although undocumented, LambertW[k, z] autoevaluates to ProductLog[k, z] in the Wolfram Language.

Abel polynomial | digit-shifting constants | Lambert's transcendental equation | omega constant | power tower