Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Mittag-Leffler series for generating continuum sum?
(12/12/2009, 08:18 PM)mike3 Wrote: *sighs* I guess its back the drawing board, then. This continuum sum thing seems really difficult to generalize to arbitrary analytic functions, as is needed for tetration.

Well, even if there was a simple Mittag-Leffler expansion, the chance to have luck with a convergent Faulhaber application, was anyway quite low, wasnt it? If not even entire the continuum sum of exp(exp(x)) was convergent.

Hm, so summarizing:
exp(x) has a convergent Faulhaber sum.
non-entire functions have no convergent Faulhaber sum.
functions with over-exponential growth (like exp(exp(x))) have probably no convergent Faulhaber sum.
However if there was a way to rearrange the terms, there might convergence be possible (as you greatly showed with exp(exp(x)) and 1/(x+1)).

But then my question would be whether the value depends on how the terms are rearranged (I mean not only giving different branches, but a continuum of solutions).

Messages In This Thread
RE: Mittag-Leffler series for generating continuum sum? - by bo198214 - 12/12/2009, 09:53 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Perhaps a new series for log^0.5(x) Gottfried 3 2,981 03/21/2020, 08:28 AM
Last Post: Daniel
Question Taylor series of i[x] Xorter 12 18,977 02/20/2018, 09:55 PM
Last Post: Xorter
  Recursive formula generating bounded hyper-operators JmsNxn 0 2,568 01/17/2017, 05:10 AM
Last Post: JmsNxn
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 19,782 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 2,607 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 2,660 12/21/2016, 01:27 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 20,792 08/28/2016, 08:52 PM
Last Post: sheldonison
  2015 Continuum sum conjecture tommy1729 3 5,417 05/26/2015, 12:24 PM
Last Post: tommy1729
  [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 56,256 03/27/2015, 11:28 PM
Last Post: tommy1729
  Another way to continuum sum! JmsNxn 6 9,613 06/06/2014, 05:09 PM
Last Post: MphLee

Users browsing this thread: 1 Guest(s)