These compute the secondary real-valued branch of the Lambert W function, W_{-1}(x).
Lambert\’s W functions, W(x), are defined to be solutions of the equation W(x) \exp(W(x)) = x. This function has multiple branches for x < 0; however, it has only two real-valued branches. We define W_0(x) to be the principal branch, where W > -1 for x < 0, and W_{-1}(x) to be the other real branch, where W < -1 for x < 0.
err contains an estimate of the absolute error in the value z.
This function is from the GNU Scientific Library, see http://www.gnu.org/software/gsl/ for documentation.
Package: gsl