Mittag-Leffler series for generating continuum sum?
#21
Geez, the number of terms in that puppy grows up insanely fast! \( g_4 \) already has over a trillion terms... Is there any way to actually "use" this formula? Especially if we put in the Bernoulli polynomials for the continuum sum, then the number of terms gets even bigger and it gets even hairier(!). So I'd be curious if this is the same as the other formula (the one supposedly mentioned in the 1905 book) or not.

EDIT: got that wrong, that's a trillion operations not terms. The maximum degree for \( g_4 \) is just \( 4^{2*4} + 4^{2*3} + 4^{2*2} + 4^{2*1} = 69904 \) Smile But still, it's a lot of operations!
Reply


Messages In This Thread
RE: Mittag-Leffler series for generating continuum sum? - by mike3 - 12/11/2009, 11:45 AM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Divergent Series and Analytical Continuation (LONG post) Caleb 54 74,115 03/18/2023, 04:05 AM
Last Post: JmsNxn
  double functional equation , continuum sum and analytic continuation tommy1729 6 12,667 03/05/2023, 12:36 AM
Last Post: tommy1729
  Discussion on "tetra-eta-series" (2007) in MO Gottfried 40 53,592 02/22/2023, 08:58 PM
Last Post: tommy1729
  Another way to continuum sum! JmsNxn 8 28,079 02/08/2023, 03:49 AM
Last Post: JmsNxn
Question Tetration Asymptotic Series Catullus 18 28,806 07/05/2022, 01:29 AM
Last Post: JmsNxn
Question Formula for the Taylor Series for Tetration Catullus 8 16,928 06/12/2022, 07:32 AM
Last Post: JmsNxn
  Calculating the residues of \(\beta\); Laurent series; and Mittag-Leffler JmsNxn 0 4,412 10/29/2021, 11:44 PM
Last Post: JmsNxn
  Trying to find a fast converging series of normalization constants; plus a recap JmsNxn 0 4,213 10/26/2021, 02:12 AM
Last Post: JmsNxn
  Reducing beta tetration to an asymptotic series, and a pull back JmsNxn 2 8,164 07/22/2021, 03:37 AM
Last Post: JmsNxn
  Perhaps a new series for log^0.5(x) Gottfried 3 12,177 03/21/2020, 08:28 AM
Last Post: Daniel



Users browsing this thread: 2 Guest(s)