So here is a link to the updated document. I've added a little bit on non-integer iteration of the [x] operator as well as [x] for non-integer x. I used the results to write matlab code that plots \( [x]^n a \) over ranges of a, n, and x values. The plots are also in the document. There are still some limitations, but the expansion method (See http://arxiv.org/pdf/hep-th/9707206v2.pdf, pg.31) seems to work very well for x<3 and a,n<2. \( [x]^n a \) blows up for larger values of a and/or n, as expected, and the expansion produces poor results for x>3, since I currently only know inverse operations for [1], [2], and [3], and so my expansions for non-integer x are limited to 4 terms.
Plot over a:
Plot over n:
Plot over x:
Plot over a:
Plot over n:
Plot over x: