Re: exp(x) + k x = 0; analytic solution

Per Abrahamsen wrote:

I can easily convince myself that there is exactly one solution when k
0, but does it have a nice analytical solution, or do I have to use
numeric methods?

I apologize if this is the wrong place to ask.

The analytic solution returned by Mathematica 6.0.1 for k positive and x real is in terms of *ProductLog* (principal value of the Lambert W-function in Mathematica. See http://mathworld.wolfram.com/LambertW-Function.html)

In[1]:= Reduce[{Exp[x] + k x == 0, k > 0}, x, Reals]

Out[1]= k > 0 && x == -ProductLog[1/k]

Regards,
--
Jean-Marc
.