Dmitrii Kouznetsov's Tetration Extension

[bo198214]

Bo, I got your message about base b=e^(1/e) and b=sqrt(2). In these cases, the real part of quasiperiod is zero, and I cannot run my algorithm as is. I need to adopt it. It will take time. I do not think that b=sqrt(2) is of specific interest (just integer L(b)=4); we need to consider the general case.

\( b=\sqrt{2} \) is indeed only of interest because it has a simple (integer) fixed point 2. So that is our standard reference (on this forum) base to compare two different methods of computing a tetration. As for example real regular iteration/tetration is no more possible for \( b>e^{1/e} \) because there is no real fixed point.

You may advance faster than I do. You may begin with the plot of the asymptotic period T(b) and analysis of its limiting behavior in vicinity of b=1 and b=e^(1/e). Please, provide the good approximation for (at least) the leading terms.

yeah, I am also not that richly blessed with time. I will see, what I can do.

P.S. you may also correct misprints in your post:
invert the scaling factor for the argument of sin, and
delete the expression with unmatched parenthesis.

blush (again!).