Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Iteration series: Series of powertowers - "T- geometric series"
#11
(02/03/2012, 08:07 PM)Gottfried Wrote: ..(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

Quote:
Quote: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.

Quote:But perhaps there is something I can help with...
Yes, of course! A lot of.

Quote:
Quote:..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..
Reply


Possibly Related Threads...
Thread Author Replies Views Last Post
  Perhaps a new series for log^0.5(x) Gottfried 3 3,232 03/21/2020, 08:28 AM
Last Post: Daniel
Question Taylor series of i[x] Xorter 12 19,661 02/20/2018, 09:55 PM
Last Post: Xorter
  Semi-exp and the geometric derivative. A criterion. tommy1729 0 2,358 09/19/2017, 09:45 PM
Last Post: tommy1729
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 20,479 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 2,735 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 2,786 12/21/2016, 01:27 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 21,522 08/28/2016, 08:52 PM
Last Post: sheldonison
  Tetration series for integer exponent. Can you find the pattern? marraco 20 25,816 02/21/2016, 03:27 PM
Last Post: marraco
  [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 57,909 03/27/2015, 11:28 PM
Last Post: tommy1729
  [integral] How to integrate a fourier series ? tommy1729 1 4,094 05/04/2014, 03:19 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)