• ← LambertW

ProductLog

WMA link

ProductLog[z]

returns the principle solution for w in $z == wE^w$.

ProductLog[k, z]

gives the k-th solution.

The defining equation:

• • z == ProductLog[z] * E ^ ProductLog[z]

Some special values:

• • ProductLog[0]

• • ProductLog[E]

• • ProductLog[-1.5]

The graph of ProductLog:

• • Plot[ProductLog[x], {x, -1/E, E}]

  • $$\textcolor{red}{}$$