open problems / Discussion

[Gottfried]

What about the branches of Lambert-W ?

Dont know. But the interesting thing is that the lower real fixed point is preferred. To achieve a different branch of the Lambert W function you have to chose a different matrix/function.

No, that's not what I meant, but may well be it's not useful.

The same carleman-matrix C can be decomposed using the different fixpoints. So we have the impossibility: the same trace of C must equal two different geometric sums (of different diagonals using different u, in case of b=sqrt(2) of 1/(1-log(2)) and 1/(1-2log(2)).

What I had in mind was, whether at least the derivation of the W'-formula allows the same solution using different u, by considering different branches.
This would not resolve the impossibility, but it were an interesting detail.