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 Bounded Analytic Hyper operators fivexthethird Junior Fellow Posts: 9 Threads: 3 Joined: Nov 2013 03/25/2015, 07:29 AM That is a fantastic paper! I have an idea on how to extend this to real bases greater than eta Define, for integer $n$, the super root $\text{srt}_n(z)$ as the inverse of tetration in the base so that we have $^n\text{srt}_n(z) = z$ Then we simply apply your method to factor this in $n$: $\vartheta(z,w) = \sum_{n=0}^{\infty} \text{srt}_{n+1}(z)\frac{w^n}{n!}$ $\text{srt}_{n+1}(z) = \frac{\mathrm{d}^n }{\mathrm{d} w^n} |_{w=0} \vartheta(z,w)$ Then we can simply invert in z. ...unfortunately, there does not seem to be a nice recursion relation between super roots that would force the result to be a tetration. But it seems to converge numerically to the super root for your tetration. « 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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