Computes the Lambert W function, giving efficient solutions to the equation x*exp(x)==x
lambertW(z, b = 0, maxiter = 10, eps = .Machine$double.eps, min.imag = 1e-09)

Usage,

`lambertW(z, b = 0, maxiter = 10, eps = .Machine$double.eps, min.imag = 1e-09)`

## Arguments

- z
(complex) vector of values for which to compute the function

- b
integer, defaults to 0. vector of branches: b=0 specifies the principal
branch, 0 and -1 are the ones that can take non-complex values

- maxiter
maximum numbers of iterations for convergence

- eps
convergence tolerance

- min.imag
maximum magnitude of imaginary part to chop when returning solutions

## Details

Compute the Lambert W function of z. This function satisfies
W(z)*exp(W(z)) = z, and can thus be used to express solutions
of transcendental equations involving exponentials or logarithms.
The Lambert W function is also available in
Mathematica (as the ProductLog function), and in Maple and Wolfram.

## References

Corless, Gonnet, Hare, Jeffrey, and Knuth (1996), "On the Lambert
W Function", Advances in Computational Mathematics 5(4):329-359

## Author

Nici Schraudolph <schraudo at inf.ethz.ch> (original
version (c) 1998), Ben Bolker (R translation)
See <https://stat.ethz.ch/pipermail/r-help/2003-November/042793.html>