ProductLog[z] gives the principal solution for in .
ProductLog[k, z] gives the solution.
Mathematical function (see Section A.3.10).
The solutions are ordered according to their imaginary parts.
For , ProductLog[z] is real.
ProductLog[z] satisfies the differential equation .
ProductLog[z] has a branch cut discontinuity in the complex z plane running from to . ProductLog[k, z] for integer has a branch cut discontinuity from to .
See The Mathematica Book: Section 3.2.10.
See also: Log.