• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Tetra-series andydude Long Time Fellow Posts: 509 Threads: 44 Joined: Aug 2007 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. « Next Oldest | Next Newest »

 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 Taylor series of i[x] Xorter 12 10,124 02/20/2018, 09:55 PM Last Post: Xorter Taylor series of cheta Xorter 13 10,796 08/28/2016, 08:52 PM Last Post: sheldonison Derivative of E tetra x Forehead 7 8,597 12/25/2015, 03:59 AM Last Post: andydude [integral] How to integrate a fourier series ? tommy1729 1 2,284 05/04/2014, 03:19 PM Last Post: tommy1729 Iteration series: Series of powertowers - "T- geometric series" Gottfried 10 15,592 02/04/2012, 05:02 AM Last Post: Kouznetsov Iteration series: Different fixpoints and iteration series (of an example polynomial) Gottfried 0 2,654 09/04/2011, 05:59 AM Last Post: Gottfried What is the convergence radius of this power series? JmsNxn 9 14,786 07/04/2011, 09:08 PM Last Post: JmsNxn An alternate power series representation for ln(x) JmsNxn 7 12,852 05/09/2011, 01:02 AM Last Post: JmsNxn weird series expansion tommy1729 2 3,993 07/05/2010, 07:59 PM Last Post: tommy1729 Something interesting about Taylor series Ztolk 3 6,049 06/29/2010, 06:32 AM Last Post: bo198214

Users browsing this thread: 1 Guest(s)