# LambertW0

Name:
LambertW0 - principal branch of the Lambert-W function
Synopsis:
   double LambertW0 -> double

Examples:
      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 )       Version: 090818

Description:
   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    growing x.       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    of SLI.

References:
    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,    329--359.     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.

Author:
Diesmann

SeeAlso: Source:
/home/graber/work-nest/nest-git/nest-simulator/lib/sli/mathematica.sli