Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Transseries, nest-series, and other exotic series representations for tetration
Hmm. I think I may have figured out what's going on. It seems like Faulhaber's formula fails to sum

for what appears to be . Below that it works and sums it to, apparently . So that would provide an analytic continuation to higher q-values, thus the formula given is valid in a sense, but direct application of the Faulhaber formula will not work. It seems that a combination of analytic continuation and divergent summation theory applied to Faulhaber and transseries theory is needed to put together a comprehensive theory of continuum sums of general analytic functions.

I find the appearance of interesting, considering it is the magnitude of the imaginary period of the exponential function. I don't know if that is significant or not.

Messages In This Thread

Possibly Related Threads...
Thread Author Replies Views Last Post
Question Taylor series of i[x] Xorter 12 10,602 02/20/2018, 09:55 PM
Last Post: Xorter
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 10,890 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 1,481 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,341 12/21/2016, 01:27 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 11,420 08/28/2016, 08:52 PM
Last Post: sheldonison
  Tetration series for integer exponent. Can you find the pattern? marraco 20 15,518 02/21/2016, 03:27 PM
Last Post: marraco
  [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 35,777 03/27/2015, 11:28 PM
Last Post: tommy1729
  [2014] Representations by 2sinh^[0.5] tommy1729 1 2,208 11/16/2014, 07:40 PM
Last Post: tommy1729
  [integral] How to integrate a fourier series ? tommy1729 1 2,367 05/04/2014, 03:19 PM
Last Post: tommy1729
  Wonderful new form of infinite series; easy solve tetration JmsNxn 1 4,204 09/06/2012, 02:01 AM
Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)