# LambertW

Command: LambertW

Synopsis

double double LambertW -> double
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.

File
lib/sli/mathematica.sli
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.

Author
Diesmann
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.