# LambertW

##### 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.

If any entries of `x`

are infinite or `NA`

, the corresponding
results are `NA`

.

##### 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.

##### Examples

```
# NOT RUN {
LambertW(exp(1))
# }
```

*Documentation reproduced from package spatstat, version 1.57-1, License: GPL (>= 2)*