LambertW0 - principal branch of the Lambert-W functionSynopsis:
double LambertW0 -> double
The Lambert-W function has applications in many areas as described in  and .
For example, the solution of
exp(s) = 1 + a*s
with respect to s can be written in closed form as
s=1/a * (-aW(-exp(-1/a)/a) -1 )
The Lambert-W function  is the inverse function of x=W*exp(W). For real values of
x and W, the function W(x) is defined on [-1/e,\infty). On the interval [-1/e,0)
it is double valued. The two branches coincide at W(-1/e)=-1. The so called
principal branch LambertW0 continuously grows (W>=-1) and crosses the origin (0,0).
The non-principal branch LambertWm1 is defined on [-1/e,0) and declines to -\infty for
NEST uses the GSL  implementations of LambertW0 and LambertWm1 if available and
falls back to to the iterative scheme LambertW suggested in  if not.
The GSL interfaces for LambertW0 and LambertWm1 are in the SpecialFunctionsModule
 Corless, R. M., Gonnet, G. H., Hare, D. E. G., Jeffrey, D. J., & Knuth, D. E.
(1996). On the lambert w function. Advances in Computational Mathematics 5,
 Galassi, M., Davies, J., Theiler, J., Gough, B., Jungman, G., Booth, M.,
& Rossi, F. (2006). GNU Scientific Library Reference Manual (2nd Ed.).
Network Theory Limited.
 Wikipedia (2009). Lambert W function ---wikipedia, the free encyclopedia.