the inconsistency depending on fixpoint-selection

[Gottfried]

There is lots of other interesting stuff in Knoebel's article, but read it yourself

Yes, I've read it several times, and with the growth of my knowledge I understand increasingly more. There may still be something of whose relevance I didn't got aware yet...

For our consideration here let:
and so that . So I wonder whether we can express ( and are indeed bijective) with the Lambert W function. Any ideas?

Hmm, I'll have to study this first a bit more.