gives the principal solution for w in .

gives the k^(th) solution.


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The solutions are ordered according to their imaginary parts.
  • For , ProductLog[z] is real.
  • ProductLog[z] satisfies the differential equation .
  • For certain special arguments, ProductLog automatically evaluates to exact values.
  • ProductLog can be evaluated to arbitrary numerical precision.
  • ProductLog automatically threads over lists.
  • 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 0.
Introduced in 1996