Tetra-series

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Tetra-series

andydude $Offline$
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Posts: 509
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#25

10/31/2009, 09:37 PM (This post was last modified: 10/31/2009, 09:40 PM by andydude.)

(10/31/2009, 02:40 PM)Gottfried Wrote: Check, for base x=1/2 I get AS(x) = 0.938253002500

Yes, with the average of the two series, I get AS(0.5) = 0.938253.

The way that I got the coefficients is slightly different than your method. I did this:
Let $\mathbf{B}$ be a matrix defined by $B_{jk} = \frac{1}{j!} \text{spow}_k^{(j)}(1)$ , and let
$ \begin{tabular}{rl} f(x) & = \sum_{k=1}^\infty f_k (x - 1)^k \\ & = \sum_{k=1}^\infty g_k ({}^{k}x) \\ F &= (f_0, f_1, f_2, ...)^T \\ G &= (g_0, g_1, g_2, ...)^T \\ \end{tabular} $
then
$\mathbf{B}.F = G$
so I thought, if we know G (1, -1, 1, -1, ...), then
$F = \mathbf{B}^{-1}G$
and when the matrix size is even I get the first series, and when the matrix size is odd, I get the second series.

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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

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