06/04/2017, 02:07 PM
(This post was last modified: 06/07/2017, 08:46 PM by sheldonison.)

James,

I had to edit my posts to remove any references to Kneser's function. I can get as far as Kneser's RiemannMapping region, which exactly matches Jay's post. And, if you reread my edited posts, I showed that you can get from the RiemannMapping region as follows:

Then you can use the complex valued inverse Abel function to get Tetration as follows:

But I don't understand Kneser's function which does not seem to be . Kneser is using the RiemannMapping result in a different way than I am. Also, Kneser finishes by constructing the real valued slog.... This thread is still good and the pictures are really cool, but I am discouraged that after all these years I still don't understand Kneser as much as I would like. I'm sure that in time, I will understand more, or perhaps someone can step in and further enlighten me.

I think maybe I got it, but I will need to reread Henryk's post a few more times. The only thing I can figure, that makes any sense at all is:

Kneser's equation for the inverse of Tetration in terms of tau

This shows the inverse of tau in terms of my z+theta(z)

But then is the end result of the inverse of the RiemannMapping, which totally I don't get from Henryk's post, and it still confuses me....

can also be expressed as a different 1-cyclic mapping I'm not sure this matter much though

I had to edit my posts to remove any references to Kneser's function. I can get as far as Kneser's RiemannMapping region, which exactly matches Jay's post. And, if you reread my edited posts, I showed that you can get from the RiemannMapping region as follows:

Then you can use the complex valued inverse Abel function to get Tetration as follows:

But I don't understand Kneser's function which does not seem to be . Kneser is using the RiemannMapping result in a different way than I am. Also, Kneser finishes by constructing the real valued slog.... This thread is still good and the pictures are really cool, but I am discouraged that after all these years I still don't understand Kneser as much as I would like. I'm sure that in time, I will understand more, or perhaps someone can step in and further enlighten me.

I think maybe I got it, but I will need to reread Henryk's post a few more times. The only thing I can figure, that makes any sense at all is:

Kneser's equation for the inverse of Tetration in terms of tau

This shows the inverse of tau in terms of my z+theta(z)

But then is the end result of the inverse of the RiemannMapping, which totally I don't get from Henryk's post, and it still confuses me....

can also be expressed as a different 1-cyclic mapping I'm not sure this matter much though

- Sheldon