05/02/2010, 09:12 AM

Might I also point your attention to this post, in which I actually give some coefficients of pentation.

Also, I'd like to point your attention to these pictures of tetration's fixedpoints in the complex plane (which is listed as exp^z(1) - z).

As you can see, there are 3 fixed points for base-e, 2 are complex conjugates of each other as in tetration, and 1 is "lower" as you put it. The coefficients I calculated above are calculated with natural/intuitive iteration, so there is not explicit fixedpoint in the calculation.

I forgot what I was going to say next.

Also, I'd like to point your attention to these pictures of tetration's fixedpoints in the complex plane (which is listed as exp^z(1) - z).

As you can see, there are 3 fixed points for base-e, 2 are complex conjugates of each other as in tetration, and 1 is "lower" as you put it. The coefficients I calculated above are calculated with natural/intuitive iteration, so there is not explicit fixedpoint in the calculation.

I forgot what I was going to say next.