01/13/2008, 08:43 AM

It has become large.

I think our intent is to make this a short introduction, not a full book on tetration, but at least the version I'm posting today has grown in length from the version Henryk started this thread with, but Henryk's content still needs to be merged in with this content. I have included Henryk's introduction, and in the file I have indicated where Henryk's sections would fit in with this outline.

In the version that I am posting, I have included many of my own results, results which are easy to verify, and results that do not need a great deal of mathematical background to verify. This is a list of my own work I have included:

Of all of these, the theorem I was most reluctant to include is the Taylor series of tetration and iterated exponentials (pages 21-22). This recurrence equation took me several months of research to find, and as such, I want a little credit for it, but thats all. I have other results that could be much more valuable for publication, so I decided to include this recurrence equation after all.

Much of the content, like reviews of other people's work, I had actually written some time before, and was planning on writing a book about Tetration. Although this never happened, I thought these sections were appropriate for a FAQ, so I have included some of these sections verbatim. Since the topological conjugacy section involves commutative diagrams, I have included the package (diagrams.sty) in the folder I uploaded. Also included are the images used within the FAQ.

To everyone: please look over the material, see what you can improve, and what is missing, wrong, inappropriate, too advanced, misplaced, out of order, and so on. We may have to split this into two articles again, one for the FAQ and one for the collection of theorems, but I like the idea of having a single article to describe our progress.

Andrew Robbins

PS. If you don't want the sources, just download the PDF.

I think our intent is to make this a short introduction, not a full book on tetration, but at least the version I'm posting today has grown in length from the version Henryk started this thread with, but Henryk's content still needs to be merged in with this content. I have included Henryk's introduction, and in the file I have indicated where Henryk's sections would fit in with this outline.

In the version that I am posting, I have included many of my own results, results which are easy to verify, and results that do not need a great deal of mathematical background to verify. This is a list of my own work I have included:

- Derivation of Munafo class using super-logarithms.

- Extending hyper-N-operations to real number N.

- Extending hyper-N-logarithms to real number N.

- Extending Galidakis' Puiseux series to iterated exponentials. (trivial)

- My Recurrence equation for Taylor series of tetration.

- My Recurrence equation for Taylor series of iterated exponentials.

- Topological conjugacy of exp., dec. exp., and scaled exp. (Exponential-like conjugates).

- Topological conjugacy of prod. exp., self-power, and self-root (Lambert-like conjugates).

Of all of these, the theorem I was most reluctant to include is the Taylor series of tetration and iterated exponentials (pages 21-22). This recurrence equation took me several months of research to find, and as such, I want a little credit for it, but thats all. I have other results that could be much more valuable for publication, so I decided to include this recurrence equation after all.

Much of the content, like reviews of other people's work, I had actually written some time before, and was planning on writing a book about Tetration. Although this never happened, I thought these sections were appropriate for a FAQ, so I have included some of these sections verbatim. Since the topological conjugacy section involves commutative diagrams, I have included the package (diagrams.sty) in the folder I uploaded. Also included are the images used within the FAQ.

To everyone: please look over the material, see what you can improve, and what is missing, wrong, inappropriate, too advanced, misplaced, out of order, and so on. We may have to split this into two articles again, one for the FAQ and one for the collection of theorems, but I like the idea of having a single article to describe our progress.

Andrew Robbins

PS. If you don't want the sources, just download the PDF.