Tetra-series
#22
(10/31/2009, 10:38 AM)andydude Wrote: This is probably an old result. For the function

\( AS(x) = \sum_{k=0}^{\infty} (-1)^k ({}^{k}x) \)

I found using Carleman matrices that

\( AS(x+1) = 1 + x^2 + \frac{1}{2}x^3 + \frac{4}{3}x^4 + \frac{19}{12}x^5 + \cdots \)

is this related to the series above?

Hmmm, don't recognize this coefficients. Would you mind to show more of your computations?
Gottfried Helms, Kassel
Reply


Messages In This Thread
Tetra-series - by Gottfried - 11/20/2007, 12:47 PM
RE: Tetra-series - by andydude - 11/21/2007, 07:14 AM
RE: Tetra-series - by Gottfried - 11/22/2007, 07:04 AM
RE: Tetra-series - by andydude - 11/21/2007, 07:51 AM
RE: Tetra-series - by Gottfried - 11/21/2007, 09:41 AM
RE: Tetra-series - by Ivars - 11/21/2007, 03:58 PM
RE: Tetra-series - by Gottfried - 11/21/2007, 04:37 PM
RE: Tetra-series - by Gottfried - 11/21/2007, 06:59 PM
RE: Tetra-series - by andydude - 11/21/2007, 07:24 PM
RE: Tetra-series - by Gottfried - 11/21/2007, 07:49 PM
RE: Tetra-series - by andydude - 11/21/2007, 08:39 PM
RE: Tetra-series - by Gottfried - 11/23/2007, 10:47 AM
RE: Tetra-series - by Gottfried - 12/26/2007, 07:39 PM
RE: Tetra-series - by Gottfried - 02/18/2008, 07:19 PM
RE: Tetra-series - by Gottfried - 06/13/2008, 07:15 AM
RE: Tetra-series - by Gottfried - 06/22/2008, 05:25 PM
Tetra-series / Inverse - by Gottfried - 06/29/2008, 09:41 PM
RE: Tetra-series / Inverse - by Gottfried - 06/30/2008, 12:11 PM
RE: Tetra-series / Inverse - by Gottfried - 07/02/2008, 11:01 AM
RE: Tetra-series / Inverse - by andydude - 10/31/2009, 10:38 AM
RE: Tetra-series / Inverse - by andydude - 10/31/2009, 11:01 AM
RE: Tetra-series / Inverse - by Gottfried - 10/31/2009, 01:25 PM
RE: Tetra-series / Inverse - by Gottfried - 10/31/2009, 02:40 PM
RE: Tetra-series / Inverse - by andydude - 10/31/2009, 09:37 PM
RE: Tetra-series / Inverse - by Gottfried - 10/31/2009, 10:33 PM
RE: Tetra-series / Inverse - by Gottfried - 11/01/2009, 07:45 AM
RE: Tetra-series / Inverse - by andydude - 11/03/2009, 03:56 AM
RE: Tetra-series / Inverse - by andydude - 11/03/2009, 04:12 AM
RE: Tetra-series / Inverse - by andydude - 11/03/2009, 05:04 AM
RE: Tetra-series / Inverse - by Gottfried - 10/31/2009, 12:58 PM

Possibly Related Threads…
Thread Author Replies Views Last Post
  Divergent Series and Analytical Continuation (LONG post) Caleb 54 68,392 03/18/2023, 04:05 AM
Last Post: JmsNxn
  Discussion on "tetra-eta-series" (2007) in MO Gottfried 40 49,384 02/22/2023, 08:58 PM
Last Post: tommy1729
Question Is the Tetra-Euler Number Rational? Catullus 1 3,973 07/17/2022, 06:37 AM
Last Post: JmsNxn
Question Tetration Asymptotic Series Catullus 18 26,584 07/05/2022, 01:29 AM
Last Post: JmsNxn
Question Natural Properties of the Tetra-Euler Number Catullus 6 11,795 07/01/2022, 08:16 AM
Last Post: Catullus
Question Formula for the Taylor Series for Tetration Catullus 8 15,735 06/12/2022, 07:32 AM
Last Post: JmsNxn
  Calculating the residues of \(\beta\); Laurent series; and Mittag-Leffler JmsNxn 0 4,182 10/29/2021, 11:44 PM
Last Post: JmsNxn
  Trying to find a fast converging series of normalization constants; plus a recap JmsNxn 0 3,974 10/26/2021, 02:12 AM
Last Post: JmsNxn
  Reducing beta tetration to an asymptotic series, and a pull back JmsNxn 2 7,695 07/22/2021, 03:37 AM
Last Post: JmsNxn
  Perhaps a new series for log^0.5(x) Gottfried 3 11,628 03/21/2020, 08:28 AM
Last Post: Daniel



Users browsing this thread: 1 Guest(s)