I have a recommendation concerning the derivative of Lambert's W. Presently,
it is defined as
W' = exp(-W)/(W+1)
which is equivalent I believe to
W' = W/[x(W+1)],
since W(x)/x = 1/[x/W(x)] = 1/exp(W(x)) = exp(-W(x)).
However, I believe the latter form is preferable as it contains no
exponential term and thus lends itself to algebraic simplifications more
easily. Is there a reason that I may not be aware of why the first form of
the derivative was used? Are there any objections if I were to replace it
with the second form in CVS?
Viktor
-----Original Message-----
From: Barton Willis [mailto:willisb at unk.edu]
Sent: Tuesday, May 20, 2008 2:11 PM
To: Viktor T. Toth; 'Oliver Kullmann'
Cc: maxima at math.utexas.edu
Subject: Re: [Maxima] Lambert W function?
The function "lambert_w" is new to 5.15.0 (thanks due to Raymond and
Stavros).
The solve doesn't know about lambert_w. So far, lambert_w evaluates for
doubles (but not big floats):
(%i5) lambert_w(5.60);
(%o5) 1.392014569377103
(%i6) diff(lambert_w(x),x);
(%o6) %e^(-lambert_w(x))/(lambert_w(x)+1)
(%i9) taylor(lambert_w(x),x,0,4);
(%o9) x-x^2+(3*x^3)/2-(8*x^4)/3+...
Barton