06/21/2022, 10:08 PM
(06/20/2022, 05:42 PM)Gottfried Wrote:(06/18/2022, 03:25 AM)JmsNxn Wrote: ...
As Gottfried spoke, he meant that he can think of less than 5 solutions to tetration which are intrinsically unique. This is true. There is Kneser. There is Sheldon. There is Carlemann (programmed by Gottfried). There is Kouznetsov. There is Paulsen and Cowgill.
...
So, for instance, it seems to me that there is a misconception of this all when I read that "the existence of Carlemanmatrices is/must be proven" or the like... It even might be, that the Riemann-map can be formulated in that matrix-algebraic notation, I only can't say this: since I do not understand enough of this mapping at all; if it can be expressed in terms of building powerseries at all then it should be possible, and it is not needed that the occuring matrices are "Carleman", they might be "Vandermonde", or whatelse ever.
Gottfried
Sorry, when I meant Carlemann, I meant using Carlemann to produce Kneser. Carlemann for Schroder maps is actually very natural. My head gets fuzzy thinking about it for Kneser though, it just seems unnatural to me. Though, there definitely exists Carlemann matrices which solve the equation--can't imagine the construction method though.