Name: LambertW - imple iteration implementing the Lambert-W function

Synopsis:

double double LambertW -&gt; 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&gt;=-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., &amp; 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., 
&amp; Rossi, F. (2006). GNU Scientific Library Reference Manual (2nd Ed.). 
Network Theory Limited.


Author:

Diesmann


SeeAlso:

LambertWm1
LambertW0
testsuite::test_lambertw
CompileMath

Source:

/var/www/debian/nest/nest-simulator-2.20.0/lib/sli/mathematica.sli
