LambertWm1 - non-principal branch of the Lambert-W functionSynopsis:
double LambertWm1 -> double
The Lambert-W function has applications in many areas as described in  and .
For example, the problem of finding the location of the maximum of the postsynaptic
potential generated by an alpha-function shaped current can be reduced to the
exp(s) = 1 + a*s .
Here, s is the location of the maximum in scaled time s=b*t, where
b= 1/tau_alpha - 1/tau_m and a is the ratio of the time constants tau_m/tau_alpha.
In terms of the Lambda_W function the solution is
s=1/a * (-aW(-exp(-1/a)/a) -1 ) .
The solution is guaranteed to live on the non-principal branch because the scaled time
needs to be positive. This requires W < -1/a which is trivially fulfilled for the
non-principal branch and there is no solution on the principal branch.
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.