Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Mittag-Leffler series for generating continuum sum?
#25
(12/12/2009, 09:53 PM)bo198214 Wrote: 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).

I.e. given two transseries representations for an analytic function, if both converge and so do their Faulhaber continuum sums, do those sums agree whenever both converge? It would be interesting to determine this, but I'm not sure what the proof would be like.

Another thing I've wondered about is, could there be some way to assign some sort of value to the divergent sums of Faulhaber coefficients given an arbitrary power series of nonzero convergence radius as input?

Failing the Faulhaber method, could there be some other way to define continuum sum that agrees with it but covers a lot more ground?
Reply


Messages In This Thread
RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 12/13/2009, 02:48 AM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Perhaps a new series for log^0.5(x) Gottfried 3 2,634 03/21/2020, 08:28 AM
Last Post: Daniel
Question Taylor series of i[x] Xorter 12 17,964 02/20/2018, 09:55 PM
Last Post: Xorter
  Recursive formula generating bounded hyper-operators JmsNxn 0 2,435 01/17/2017, 05:10 AM
Last Post: JmsNxn
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 18,838 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 2,493 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 2,531 12/21/2016, 01:27 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 19,780 08/28/2016, 08:52 PM
Last Post: sheldonison
  2015 Continuum sum conjecture tommy1729 3 5,157 05/26/2015, 12:24 PM
Last Post: tommy1729
  [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 54,217 03/27/2015, 11:28 PM
Last Post: tommy1729
  Another way to continuum sum! JmsNxn 6 9,161 06/06/2014, 05:09 PM
Last Post: MphLee



Users browsing this thread: 1 Guest(s)