Dmitrii Kouznetsov's Tetration Extension

[Kouznetsov]

Henrik, sorry, I was sure that the page is available from anywhere.

Nono this was a misunderstanding, I can read your page. However I can not probably write on it.
I was just curious what citizendium is. It states something like the "world's most trusted encyclopedia". So is there some peer reviewing going on?

I should move it to some readable and writable place.
How about wikisource?

Seems more to be about historic texts isnt it?

1. Yes, it is. I agree. Could you register as citizendium? It seems to be the only wiki that allows original researches.

2. There are two regular superexponentials at base \( b \) such that \( 1<b<\exp(1/{\rm e}) \).
I have plotted the only one, \( F \) such that \( F(0)=1 \).
At \( b=\sqrt{2} \), for example,
\( \lim_{x \rightarrow \infty} F_{\sqrt{2}}(x+{\rm i}y)=2 \);
\( \lim_{x \rightarrow -\infty} F_{\sqrt{2}}(x+{\rm i}y)=4 \).
There is another one, \( G \) that grows up along the real axis faster than any exponential and aproaches its limiting values in the opposite direction. I am writing source for its evaluation.
3. Then we have covered the ranges \( 1<b<\exp(1/\rm e) \) and \( b>\exp(1/\rm e) \); and I think about cases \( b=\exp(1/\rm e}) \) and \( b<1 \). I suggest that you use the same idea: first, find the asymptotics and periodicity (if any); then recover the analytic function with these properties. Could you calculate some pictures (similar to those I have posted) for these cases?