Iteration series: Series of powertowers - "T- geometric series"

[Kouznetsov]

..(re-)discovery of the concept of "Carleman-matrix"
a) there is nothing known yet which would make the Carlemanmatrix-approach a unique preferable solution,
b) the solution for the fractional iterates is dependent on the fixpoint which was chosen to center the power series around, and
c) we get complex-valued power series for real valued fractional heights.

Before the Arabian (positional) system of writing numbers spread, one used the Roman numbers. There existed several ways to perform oerations +,-,*,/. I believe, some researchers wondered:"wether the result does not depend on the numeral system used?" In order to show that the question is not trivial, I loaded the "Mizugadro number", http://samlib.ru/k/kuznecow_d_j/mizugade.shtml

http://tori.ils.uec.ac.jp/TORI/index.php/Tetration
http://math.eretrandre.org/hyperops_wiki

.. their ambition seem to be very high..

Yes, while the ambitions are much higher than the level achieved.

But perhaps there is something I can help with...

Yes, of course! A lot of.

..an account at the second..

Well, that was Henryk - now that you call for him I'm getting aware that we've heard little or nothing of him lastly...

Thanks, Gottfried. Hope, Henryk will appear soon..