"Knowing" a function requires quite a few pieces of information.
Solve must be extended to find as many instances as possible of solutions
which can be expressed in terms of the Lambert W function, not just the
defining instance of W as the solution to W(x)*exp(W(x))=x.
For example, integration formulas, differentiation formulas, power series,
taylor series, products, numerical evaluation (to any precision),
simplification (special values, relations to other functions, inverses).
The Maxima design does not lend itself to a simple unified method for adding
all this information, even if it were all at one's fingertips.
A dream, going back a few decades, and revived periodically, is that one
could define a new function by (say) a differential equation, and have a
computer algebra system automatically generate all the information needed to
compute with it.
Joel Moses called this "A General Theory of Special Functions".
The most recent effort I am aware of is
http://algo.inria.fr/esf/
which does not include Lambert W.
Although Wolfram has sponsored extensive cataloging of formulas (apparently
by hand) concerning special functions, it is not clear how these could be
used by a CAS except by cutting and pasting.
> -----Original Message-----
> From: maxima-bounces at math.utexas.edu
> [mailto:maxima-bounces at math.utexas.edu] On Behalf Of Oliver Kullmann
> Sent: Tuesday, May 20, 2008 9:41 AM
> To: maxima at math.utexas.edu
> Subject: Lambert W function?
>
> Hi,
>
> it seems Maxima doesn't know the Lambert W function, see
>
> http://en.wikipedia.org/wiki/Lambert_W_function
>
> With that function one could enhance "solve" to handle
> also for example e^x - x = a.
>
> (I needed such a case, and my old Mupad implementation
> returned the solution using that W-function, which I found
> helpful.)
>
> Oliver
> _______________________________________________
> Maxima mailing list
> Maxima at math.utexas.edu
> http://www.math.utexas.edu/mailman/listinfo/maxima
>