10/18/2022, 07:13 AM
(10/18/2022, 07:06 AM)Shanghai46 Wrote:(10/18/2022, 06:37 AM)Daniel Wrote:(10/18/2022, 06:13 AM)Shanghai46 Wrote: So, we saw in the previous part a formula which can be used to calculate half (or even complex) iteration of any function which converge. (it doesn't work if it doesn't)
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Anyway, tell me what you think!
At first reading your approach appears to be valid. I know because it was the first approach I developed. I suspect others here are likewise familiar. Currently there are about half a dozen good approaches to extending tetration.
A major problem with tetration is that without wide exposure, folks reinvent the same thing over and over. One of the major papers on tetration is named Exponentials Reiterated, due to this reinvention.
I personally uploaded what I found. The problem is that it's probably the same case as for half dervivatives, where you have dozens of methods which are mathematically correct, but with different results. Also technically this method works with all numbers which infinite tetration converges. It's the red part in you diagram on your website
Well I'm not sure that techniques that give different results can both be correct, but you have identified an important step in tetration research, the categorization of the different methods and the reconciliation of their different results.
Daniel