Maximum number of iterations of third-order Halley's method.
Value
This function returns the principal branch of the $W$ function
for real $z$.
It returns $W(z) \geq -1$,
and NA for $z < -1/e$.
Details
The Lambert $W$ function is the root of the equation
$W(z) \exp(W(z)) = z$
for complex $z$.
It is multi-valued if $z$ is real and $z < -1/e$.
For real $-1/e \leq z < 0$ it has two
possible real values, and currently only the upper branch
is computed.
References
Corless, R. M. and Gonnet, G. H. and
Hare, D. E. G. and Jeffrey, D. J. and Knuth, D. E. (1996)
On the Lambert $W$ function.
Advances in Computational Mathematics,
5(4), 329--359.