Lambert W

The Lambert $W$ function is the (multi-valued) function that satisfies the equation $$z=W(z)e^{W(z)}.$$

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  Plot of the principal branch $W_0$.

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  Domain coloring of analytic continuation of branch $W_0(x)$ to $\mathbb{C}$.

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  Domain coloring of analytic continuation of branch $W_{-1}(x)$ to $\mathbb{C}$.

Videos

• 6: Recursion, Infinite Tetrations and the Lambert W Function (4 August 2014)

External links

• Having fun with the Lambert $W(x)$ function

See also

Lambert W0
Lambert W1

References

• R. M. Corless, G. H. Gonnet, D.E.G. Hare and D.E. Knuth: On the Lambert W function (1996)... (previous)... (next) $(1.5)$