Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Mittag-Leffler series for generating continuum sum?
The idea is that maybe if Faulhaber's formula does not yield a convergent formula when applied directly to a Taylor series with finite convergence radius, perhaps it would if we could apply it to a Mittag-Leffler series or some other extension of the Taylor series to a cut plane. The reasoning being that the "reason it does not converge" (if you go and read the thread "Continuum sum formula rescued?", I mention this there) may be that the Taylor series doesn't look "globally" like the function it represents due to the limited convergence (and the partial sums of it don't approach, on a "global scale", the function), while th Mittag-Leffler extension would, and thus maybe the Faulhaber formula will succeed there, when it failed on the Taylor series. But I can't give it a shot, without being able to compute that formula. My first test would be to try finding the Mittag-Leffler expansion for log(1 + z) (Taylor series at 0 is the Mercator series), and then apply Faulhaber's formula and see if we get convergence to the log-factorial.

Messages In This Thread
RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 11/14/2009, 08:24 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Perhaps a new series for log^0.5(x) Gottfried 3 1,416 03/21/2020, 08:28 AM
Last Post: Daniel
Question Taylor series of i[x] Xorter 12 15,094 02/20/2018, 09:55 PM
Last Post: Xorter
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,949 01/17/2017, 05:10 AM
Last Post: JmsNxn
  An explicit series for the tetration of a complex height Vladimir Reshetnikov 13 15,490 01/14/2017, 09:09 PM
Last Post: Vladimir Reshetnikov
  Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 2,055 12/26/2016, 03:01 AM
Last Post: tommy1729
  2 fixpoints , 1 period --> method of iteration series tommy1729 0 2,100 12/21/2016, 01:27 PM
Last Post: tommy1729
  Taylor series of cheta Xorter 13 16,382 08/28/2016, 08:52 PM
Last Post: sheldonison
  2015 Continuum sum conjecture tommy1729 3 4,289 05/26/2015, 12:24 PM
Last Post: tommy1729
  [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 46,803 03/27/2015, 11:28 PM
Last Post: tommy1729
  Another way to continuum sum! JmsNxn 6 7,805 06/06/2014, 05:09 PM
Last Post: MphLee

Users browsing this thread: 1 Guest(s)