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ProductLog

ProductLog[z]
gives the principal solution for w in z=w​e^w.
ProductLog[k, z]
gives the k^(th) solution.
  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • The solutions are ordered according to their imaginary parts.
  • ProductLog[z] satisfies the differential equation d​w/d​z=w/(z(1+w)).
  • For certain special arguments, ProductLog automatically evaluates to exact values.
  • ProductLog can be evaluated to arbitrary numerical precision.
  • ProductLog[z] has a branch cut discontinuity in the complex z plane running from -∞ to -1/e. ProductLog[k, z] for integer k>0 has a branch cut discontinuity from -∞ to 0.
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