Difference between revisions of "Lambert W"
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| − | The Lambert $W$ function is the (multi-valued) | + | __NOTOC__ |
| + | The Lambert $W$ function is the (multi-valued) function that satisfies the equation | ||
| + | $$z=W(z)e^{W(z)}.$$ | ||
<div align="center"> | <div align="center"> | ||
<gallery> | <gallery> | ||
| − | File:Lambertw0plot.png|Plot of the principal branch $W_0 | + | File:Lambertw0plot.png|Plot of the principal branch $W_0$. |
File:Complexlambertw0.png|[[Domain coloring]] of [[analytic continuation]] of branch $W_0(x)$ to $\mathbb{C}$. | File:Complexlambertw0.png|[[Domain coloring]] of [[analytic continuation]] of branch $W_0(x)$ to $\mathbb{C}$. | ||
File:Complexlambertw-1.png|[[Domain coloring]] of [[analytic continuation]] of branch $W_{-1}(x)$ to $\mathbb{C}$. | File:Complexlambertw-1.png|[[Domain coloring]] of [[analytic continuation]] of branch $W_{-1}(x)$ to $\mathbb{C}$. | ||
</gallery> | </gallery> | ||
</div> | </div> | ||
| + | |||
| + | =Properties= | ||
| + | |||
| + | =Videos= | ||
| + | *[https://www.youtube.com/watch?v=AJD8kh3DSAM 6: Recursion, Infinite Tetrations and the Lambert W Function (4 August 2014)] | ||
| + | |||
| + | =External links= | ||
| + | *[http://arxiv.org/pdf/1003.1628.pdf Having fun with the Lambert $W(x)$ function] | ||
| + | |||
| + | =See also= | ||
| + | [[Lambert W0]]<br /> | ||
| + | [[Lambert W1]]<br /> | ||
=References= | =References= | ||
| − | + | * {{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]] | [[Category:SpecialFunction]] | ||
Latest revision as of 18:24, 16 June 2018
The Lambert $W$ function is the (multi-valued) function that satisfies the equation $$z=W(z)e^{W(z)}.$$
Plot of the principal branch $W_0$.
Domain coloring of analytic continuation of branch $W_0(x)$ to $\mathbb{C}$.
Domain coloring of analytic continuation of branch $W_{-1}(x)$ to $\mathbb{C}$.
Properties
Videos
External links
See also
References
- R. M. Corless, G. H. Gonnet, D.E.G. Hare and D.E. Knuth: On the Lambert W function (1996)... (previous)... (next) $(1.5)$
