Hi. Yes, it isn't analytic extension, but is unique extension. In fact the "ultra power" and "ultra exponential function" are gotten as the next step of the serial binary operations: addition, multiplication and power. I think you enjoy it if you get and read the original paper. You can see its abstract in the following site:
http://www.informaworld.com/smpp/content...order=page
I found this forum just by the google , while I was searching about the ultra exponential function, ultra power, tetration, etc.
http://www.informaworld.com/smpp/content...order=page
I found this forum just by the google , while I was searching about the ultra exponential function, ultra power, tetration, etc.

