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 the inconsistency depending on fixpoint-selection Gottfried Ultimate Fellow Posts: 810 Threads: 123 Joined: Aug 2007 02/07/2008, 09:49 PM (This post was last modified: 02/07/2008, 09:50 PM by Gottfried.) GFR Wrote:I think that the two real h's (of the t's) corresponding to the same b = sqrt(2), this time only with the + sign (sorry, Bo, ... it's the age), i.e. h = 2 and h = 4 must be different indeed. Any ... serious serial development should indeed show this situation. We cannot think that we may start from b = sqrt(2) and than, ... bingo! ... we suddely have two different values. The "strange object" that we may call h or t is the result of the application of a "two-valued function". But, two-valued "functions" are not politically correct animals. But, perhaps, I don't understand what you precisely said. I didn't sleep well, last night. I shall improve! Tomorrow is another day. GFRHi Gianfranco - I've begun a short consideration of the multivalued log(1+x)-function in the context of matrix-operations (extended version of ContinuousIteration, which may of interest. It seems interesting, but it exhibits, that we also need a more general notion of divergent summation, especially for the complex case. Since Euler-Summation (although principally able) is not well suited (and apparently not much studied) for the complex case, I'm always at the edge of possibilities. At least I cannot proceed much more without finding a reliable base for such summation-concepts. It seems, that all (or nearly all) fractional iterations of tetration, (if based on powerseries) produce hypergeometric divergent powerseries with convergence radius zero, not only the x->exp(x)-1 version. These series cannot be Euler-summed (principally) and thus we need this concept of assigning valued to such divergent series. The powerseries for log(1+x) = x - x^2/2 + x^3/3 - + ... may be configured for multivaluedness by log_k(1+x) = k*2 Pi i + x - x^2/2 + x^3/3 - + ... and the matrix-operator is then square and has all the nasty properties of divergent series. Disclaimer: all this is merely more or less speculation, and only motivated to find any usble entry-point to access the problem, which I focus in this thread. Well - have a good night, I'll stop soon, too; I've to be prepared for an exam of my statistics-class tomorrow. I'll need hawk's eyes... Kind regards - Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 03:06 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 05:20 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 10:14 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 11:17 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/04/2008, 11:25 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/04/2008, 11:32 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/04/2008, 11:43 AM RE: the inconsistency depending on fixpoint-selection - by GFR - 02/07/2008, 09:02 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 02/07/2008, 09:49 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/03/2008, 11:20 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/06/2008, 04:06 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/06/2008, 04:58 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/06/2008, 05:25 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 03:16 AM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/07/2008, 10:56 AM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 07:17 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/07/2008, 08:30 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/07/2008, 09:38 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 01:22 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 01:52 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/08/2008, 04:21 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 03/09/2008, 09:30 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 02:10 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 04:41 PM RE: the inconsistency depending on fixpoint-selection - by Gottfried - 03/14/2008, 07:19 PM RE: the inconsistency depending on fixpoint-selection - by bo198214 - 04/29/2008, 08:15 AM

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