Dmitrii Kouznetsov's Tetration Extension

[Kouznetsov]

Dmitrii, I am currently programming your tetration extension.
I just want to mention some misprints, that shouldnt go into your published paper.
In formulas (3.2), (3.3), (3.4), (3.6), (4.4) you always omit the minus sign in front of the 1 below the log. Only in the computation formula 4.2 the minus sign is at the right place.

Bo, I am glad to read from you!
Do you mean paper at http://www.ils.uec.ac.jp/~dima/PAPERS/2008analuxp.pdf ?
There is no log in formula (3.2), is there?
Now I have doubts about (3.3); I remember I had to play with phases manually combinig the logarithms; both Mathematica and Maple failed to do it as I wanted.
Can you reproduce Figure 2? Could you show it?

There may be also some simplifications (avoidance of doublification with \( L \) and \( \overline{L} \)) if you would put \( F(\overline{z})=\overline{F(z)} \) into your assumption, which is quite reasonable and which you are also using in (4.7).

Yes, I assume \( F(z^*)=F(z)^* \), but it follows from the analyticity and the assumption that \( F(z) \) is real at z>-2.

In formula (3.4),(4.4) either the \( A \) in \( {\mathcal K}_A \) should be omitted, or it should be appended whenever you use \( {\mathcal K} \)

Yes, your are right. K is always A-dependent. Better to trash this subscript.
Thank you for your comment.
I had corrected few misprints in the update
http://www.ils.uec.ac.jp/~dima/PAPERS/2008analuxp64.pdf
but not yet those you indicate; perhaps, I sould trace it again.

Dear Bo:

1. I prepare the updated version with correction of the misprints you have indicated. May I specify your real name in the Acknowledgement?

2. I have described behavior of tertation at the \( 1<\ln(b)<1/\rm e \)
at http://en.citizendium.org/wiki/User:Dmit...base._Base
Could you plot Fig.3 ? Would you like to take the text and write the rest?