Superroots and a generalization for the Lambert-W

[Gottfried]

I'm not sure if this should be in a different thread, but I just found a website with programming puzzles, and one of the puzzles is super-roots:

Hi Andy, nice to read from you... Yes the page looks interesting, I'll try to get logged in another day (I'm in bed because of some bacteria or whatever and am just lurking around here a bit).

I had already other posts with superroots, for instance that one about the power series of (1+x)^(1+x)^...^(1+x). At the moment I was involved in that question of the supperroots -1 = x^x^x and had much fun already (see http://math.stackexchange.com/questions/...38#1415538 ) but again - cannot yet complete the discussion.

Cordially -

Gottfried