# LambertW

Name:
LambertW - simple iteration implementing the Lambert-W function
Synopsis:
   double double LambertW -> double

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.       LambertW uses Halley's method described in [1] (see also [2]) to    implement the functions for the two branches LambertW0 and LambertWm1    if NEST has no access to the GSL [3].       Version: 090818

Parameters:
   The first parameter is the argument of the Lambert-W function, the    second argument is the start value of the iteration. 0.0 is a good initial    value for the principal branch of the Lambert-W function. -2.0 is a good    choice to select the non-principal branch.

References:
   [1] 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.    [2] Wikipedia (2009). Lambert W function ---wikipedia, the free encyclopedia.    [3] 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.

Author:
Diesmann

SeeAlso: Source:
/home/nest/work/nest-2.14.0/lib/sli/mathematica.sli