(08/03/2009, 08:37 AM)bo198214 Wrote: Well I thought this is obvious: The prefix "super" for a function f describes a function F with F(x+1)=f(F(x)). But super logarithm is not a superfunction of the logarithm, but an inverse superfunction of the exponential.
You're going in circles! The "super" terminology has always meant: a rank-4 function that is analogous to a rank-3 function. It was by analogy to this usage that you decided to use the "superfunction" terminology. It seems almost like a backronym to change the meaning of "super" to fit the usage in "superfunction", which I do not prefer (remember, I liked "iterational function"). I have a feeling that the push for consistent terminology will leave the corpus of writings on this forum in a state of complete inconsistency. I vote for "superlogarithm" or "Abel function of exponential". No "arcsuper".
(08/03/2009, 08:37 AM)bo198214 Wrote: Ya, think about it. I let it to you. The goal should be a motivated and understanding readerOh, I see. Ok, I could definitely use \( (g^k)_n \) in place of the Carleman matrix, that would certainly make things easier to discuss without inventing the \( D[1] \) notation. I will give it a try.
Andrew Robbins