LambertW0 - principal branch of the Lambert-W function
double LambertW0 -> double
The Lambert-W function has applications in many areas as described in [1] and [3].
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
The Lambert-W function [1] 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 [2] implementations of LambertW0 and LambertWm1 if available and
falls back to to the iterative scheme LambertW suggested in [1] if not.
The GSL interfaces for LambertW0 and LambertWm1 are in the SpecialFunctionsModule
of SLI.
[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] 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.
[3] Wikipedia (2009). Lambert W function ---wikipedia, the free encyclopedia.
Diesmann
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