Lambert W Function: Calculate W(5.67)

[mabauti]

Lambert W *edit*

How are these numbers calculated let's say W(5.67)

 

[I like Serena]

Welcome to PF, mabauti!

You can calculate W(5.67) for instance with WolframAlpha:
http://www.wolframalpha.com/input/?i=W(5.67)W can only be calculated by a numerical algorithm.
The Wolfram article about the Lambert W function gives a couple of series expansions that you can use:
http://mathworld.wolfram.com/LambertW-Function.htmlYou could also approximate it with for instance the Newton-Raphson method with $f(x)=xe^x - 5.67=0$.
That is: $x_{k+1}=x_k - {f(x_k) \over f'(x_k)}$.
Start with $x_0=2$ and you should be able to find your result to an arbitrary precision within a couple of iterations.

 

[mabauti]

great.

thanks ILS =D