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 Tetra-series Gottfried Ultimate Fellow Posts: 767 Threads: 119 Joined: Aug 2007 11/21/2007, 06:59 PM (This post was last modified: 11/22/2007, 03:58 PM by Gottfried.) Gottfried Wrote:Yes- this is a very beautiful and far-reaching fact, I think ...I've just received an answer in the newsgroup sci.math by Prof G.A.Edgar who states a numerical discrepancy between my matrix-based conjecture and termwise evaluation of the series. I cannot resolve the problem completely - the problem doesn't affect the Mb-matrix related conjectures (also of earlier date) but the problem of representation of the alternating series of powers of the reciprocal of Bb by the analoguous expression. I don't have an idea currently, how to cure this and how to correctly adapt my conjecture. So - sigh - I have to retract it for the moment. [update] I should mention, that this concerns only the Bb-matrix, which is not simply invertible. The application of the idea of the formula to other matrix-operators may be still valid; especially for triangular matrices like P the observation is still valid; I assume, it is also valid for the U-iteration x->exp(x)-1 , since the matrix-operator is the triangular Stirling-matrix. I'll check that today [/update] [update2] The problem occurs also with the U-iteration and its series of negative heights. Looks like the reciprocal matrix needs some more consideration [/update2] Gottfried P.s. I'll add the conversation here later as an attachment. [update3] A graph which shows perfect match between serial and matrix-method-summation for the Tb-series; and periodic differences between the Rb-series [/update3]     Gottfried Helms, Kassel « 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

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