ProductLog

ProductLog[z]

gives the principal solution for w in .

ProductLog[k,z]

gives the k^(th) solution.

Details

  • 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.

Examples

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Basic Examples  (3)

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Scope  (7)

Generalizations & Extensions  (3)

Applications  (9)

Properties & Relations  (5)

Possible Issues  (2)

Neat Examples  (2)

See Also

Log  Exp  FindRoot

Tutorials

Introduced in 1996
(3.0)