Difference between revisions of "Lambert W"

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Let $z \in \mathbb{C}$ and define the Lambert $W$ function by the relation $z=W(z)e^{W(z)}$. This function has two branches.
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__NOTOC__
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The Lambert $W$ function is the (multi-valued) function that satisfies the equation
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$$z=W(z)e^{W(z)}.$$
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<div align="center">
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<gallery>
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File:Lambertw0plot.png|Plot of the principal branch $W_0$.
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File:Complexlambertw0.png|[[Domain coloring]] of [[analytic continuation]] of branch $W_0(x)$ to $\mathbb{C}$.
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File:Complexlambertw-1.png|[[Domain coloring]] of [[analytic continuation]] of branch $W_{-1}(x)$ to $\mathbb{C}$.
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</gallery>
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</div>
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=Properties=
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=Videos=
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*[https://www.youtube.com/watch?v=AJD8kh3DSAM 6: Recursion, Infinite Tetrations and the Lambert W Function (4 August 2014)]
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=External links=
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*[http://arxiv.org/pdf/1003.1628.pdf Having fun with the Lambert $W(x)$ function]
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=See also=
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[[Lambert W0]]<br />
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[[Lambert W1]]<br />
  
 
=References=
 
=References=
[http://arxiv.org/pdf/1003.1628.pdf Having fun with the Lambert $W(x)$ function]
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* {{PaperReference|On the Lambert W function|1996|R. M. Corless|author2=G. H. Gonnet|author3=D.E.G. Hare|author4=D.J. Jeffrey|author4=D.E. Knuth|prev=findme|next=findme}} $(1.5)$
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[[Category:SpecialFunction]]

Latest revision as of 18:24, 16 June 2018

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

Properties

Videos

External links

See also

Lambert W0
Lambert W1

References