# LambertW

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##### Lambert's W Function

Computes Lambert's W-function.

Keywords
math
##### Usage
LambertW(x)
##### Arguments
x
Vector of nonnegative numbers.
##### Details

Lambert's W-function is the inverse function of $f(y) = y e^y$. That is, $W$ is the function such that $$W(x) e^{W(x)} = x$$

This command LambertW computes $W(x)$ for each entry in the argument x. If the library gsl has been installed, then the function lambert_W0 in that library is invoked. Otherwise, values of the W-function are computed by root-finding, using the function uniroot.

Computation using gsl is about 100 times faster.

##### Value

• Numeric vector.

##### References

Corless, R, Gonnet, G, Hare, D, Jeffrey, D and Knuth, D (1996), On the Lambert W function. Computational Mathematics, 5, 325--359. Roy, R and Olver, F (2010), Lambert W function. In Olver, F, Lozier, D and Boisvert, R (eds.), {NIST} Handbook of Mathematical Functions, Cambridge University Press.

• LambertW
##### Examples
LambertW(exp(1))
Documentation reproduced from package spatstat, version 1.28-1, License: GPL (>= 2)

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