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 Bounded Analytic Hyper operators tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 03/27/2015, 11:20 PM What I meant is that you have tetration ! Not just for the bases between 1 and eta but for all real bases larger than 1. Not sure if you realise it yet. Here is a sketchy way to show it : In short since you can interpolate analyticly x^x^... = m where ... are integer iterations and m is a real > e ... You can THUS solve for the x in tet_x(t) = m for a given m > e and t >0. ( x is the base ). But this also means that you can solve for t since you can set up the equation RAM(m,t) = x for any desired x. WHen you have this t , you have found tet_base_x(t) = m for a given m. In other words from the relation tet_x(t) = m you can solve for either x or t. therefore you can solve sexp_x(t) = m which is slog_x(m). Then invert this function and you have sexp for any base > 1. Since all of this is done analyticly you have found tetration. And it seems simpler then some other methods , like Kneser or Cauchy. Hope this is clear enough. I can explain more if required. SO JmsNxn finally has his own method , with credit to the brilliant comment of fivexthethird. ( Im thinking of a variant of this method too ) I just wonder what this will be called ... JMS method ? JN method ? Jms5x3 method ? Jms5x31729 method I already started calling it in my head " Ramanujan-Lagrange method ". The reason seems clear : Ramanujan's master theorem and Lagrange's inversion theorem. For those unfamiliar : http://en.wikipedia.org/wiki/Lagrange_inversion_theorem regards tommy1729 « Next Oldest | Next Newest »

 Messages In This Thread Bounded Analytic Hyper operators - by JmsNxn - 03/23/2015, 02:12 AM RE: Bounded Analytic Hyper operators - by MphLee - 03/24/2015, 08:34 PM RE: Bounded Analytic Hyper operators - by fivexthethird - 03/25/2015, 07:29 AM RE: Bounded Analytic Hyper operators - by marraco - 03/25/2015, 01:48 PM RE: Bounded Analytic Hyper operators - by MphLee - 03/25/2015, 07:43 PM RE: Bounded Analytic Hyper operators - by MphLee - 03/26/2015, 11:08 PM RE: Bounded Analytic Hyper operators - by tommy1729 - 03/27/2015, 09:02 AM RE: Bounded Analytic Hyper operators - by MphLee - 03/27/2015, 07:09 PM RE: Bounded Analytic Hyper operators - by tommy1729 - 03/27/2015, 11:20 PM RE: Bounded Analytic Hyper operators - by fivexthethird - 03/28/2015, 06:46 AM RE: Bounded Analytic Hyper operators - by tommy1729 - 03/28/2015, 08:59 PM RE: Bounded Analytic Hyper operators - by fivexthethird - 03/29/2015, 03:35 AM RE: Bounded Analytic Hyper operators - by tommy1729 - 03/29/2015, 04:36 PM RE: Bounded Analytic Hyper operators - by MphLee - 03/29/2015, 10:55 AM RE: Bounded Analytic Hyper operators - by tommy1729 - 03/29/2015, 04:22 PM RE: Bounded Analytic Hyper operators - by tommy1729 - 03/29/2015, 04:56 PM RE: Bounded Analytic Hyper operators - by MphLee - 03/29/2015, 07:08 PM RE: Bounded Analytic Hyper operators - by tommy1729 - 03/29/2015, 07:14 PM RE: Bounded Analytic Hyper operators - by tommy1729 - 03/29/2015, 09:37 PM RE: Bounded Analytic Hyper operators - by tommy1729 - 03/29/2015, 09:41 PM RE: Bounded Analytic Hyper operators - by JmsNxn - 03/29/2015, 11:25 PM RE: Bounded Analytic Hyper operators - by JmsNxn - 03/31/2015, 08:50 PM RE: Bounded Analytic Hyper operators - by MphLee - 03/31/2015, 09:16 PM RE: Bounded Analytic Hyper operators - by JmsNxn - 04/01/2015, 03:20 PM RE: Bounded Analytic Hyper operators - by MphLee - 04/01/2015, 06:09 PM

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