04/22/2008, 07:05 AM
Anyways, I am starting to like the <h> notation over ^(h) after all... but I was thinking of the notation for \( e^x-1 \) and I was also considering "uxp" in Kouznetsov's paper following Hooshmand's original use, and if this is going to be a general trend, we might forget using ^-^ and instead use something like "dxp" to be consistent:
as this would be both short, and correspond to current "exp" and "uxp" usage. Has this been mentioned before?
This would allow T-tetration to be written as exp_s<h>(x) and U-tetration to be written as dxp_s<h>(x).
Andrew Robbins
PS. It is interesting how "uxp" is taken, and cannot be used for U-tetration...
\(
\begin{tabular}{rl}
\exp(x) & = e^x \\
\text{uxp}(x) & = {}^{x}e \\
\text{dxp}(x) & = e^x - 1 \\
\end{tabular}
\)
\begin{tabular}{rl}
\exp(x) & = e^x \\
\text{uxp}(x) & = {}^{x}e \\
\text{dxp}(x) & = e^x - 1 \\
\end{tabular}
\)
as this would be both short, and correspond to current "exp" and "uxp" usage. Has this been mentioned before?
This would allow T-tetration to be written as exp_s<h>(x) and U-tetration to be written as dxp_s<h>(x).
Andrew Robbins
PS. It is interesting how "uxp" is taken, and cannot be used for U-tetration...