ProductLog

• 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.