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Lambert W function
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(Definition)
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Lambert's $W$ function is the inverse of the function
 given by $f(x) := x e^x$ . That is, $W(x)$ is the complex valued function that satisfies
for all
 . In practice the definition of $W(x)$ requires a branch cut, which is usually taken along the negative real axis. Lambert's W function is sometimes also called product log function.
This function allow us to solve the functional equation $$g(x)^{g(x)}=x$$ since $$g(x)=e^{W(\ln(x))}.$$
A site with good information on Lambert's W function is Corless' page ``On the Lambert W Function''
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"Lambert W function" is owned by drini. [ owner history (1) ]
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Cross-references: functional equation, real axis, negative, cut, branch, complex, inverse, function
There is 1 reference to this entry.
This is version 5 of Lambert W function, born on 2002-05-28, modified 2005-02-28.
Object id is 2957, canonical name is LambertWFunction.
Accessed 14612 times total.
Classification:
| AMS MSC: | 33B30 (Special functions :: Elementary classical functions :: Higher logarithm functions) |
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Pending Errata and Addenda
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