Hooshmand's extension of tetration

[andydude]

I feel like I have come to a resolution to this issue on my part. The way that I interpreted the definition given in Wikipedia's UXP article is that there are 2 errors, which I will cover here.

1. The fourth condition requires that between (-1) and 0, UXP' is a:
   "nondecreasing or nonincreasing" function, but this should read
   "nondecreasing and nonincreasing", which means UXP' is a constant, which means UXP is a linear function.
   
2. The closed form given in the article defines UXP as:
   \( \text{uxp}_a(x) = \exp_a^{[x+1]}(\ (x)\ ) \), but this should read
   \( \text{uxp}_a(x) = (\exp_a)^{\text{int}(x+1)}(\text{frac}(x+1)) \), because of how "frac" is implemented on some CASs, and because this is much more clear than how it is described.
   

I hope the actual reference is better than this...

Andrew Robbins