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GFR · 04/10/2008, 09:15 PM

Mmmmm ... !

andydude · 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:

$ \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...

***bo198214*** · (This post was last modified: 04/22/2008 07:25 AM by bo198214.)

andydude Wrote: $\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?

When using uxp we are no more consistent with ourselves! We agreed on using the prefixes super (for the incremented degree) and hyper (for all higher degrees) and not ultra which is anyway not a common use (only used recently by Hooshmand as far as I know). So the abbreviation would be $\text{sexp}$ .

andydude · 04/22/2008, 07:58 AM

bo198214 Wrote:So the abbreviation would be $\text{sexp}$ .

Sorry, you are right, we did agree on this. I don't know what I was thinking.

Does this mean we should use "uexp" or "dexp" instead of "dxp"?

***bo198214*** · 04/22/2008, 08:27 AM

andydude Wrote:Does this mean we should use "uexp" or "dexp" instead of "dxp"?

I am fine with dxp. It is anyway not on the same level as the super exponentiation which gives a new magnitude of growth while the decremented exponential is the same rate of growth, so there is no need to keep the same scheme (4 letters).

***bo198214*** · (This post was last modified: 04/27/2008 04:40 PM by bo198214.)

To be more specific when using a certain tetration I propose to use

nslog, nsexp for the tetration gotten by the natural Abel method aka Andrew's/Walker's method (development at 0).
dslog, dsexp for the tetration gotten by the diagonalization method (development at 0). I.e. basicly iterating $b^x$ by using the established matrix powers with real exponents on the Carlemann/Bell-Matrix.
rslog, rsexp for the tetration gotten by the regular iteration at the lower real fixed point, $e^{-e}<b<e^{1/e}$
kslog, ksexp for Dmitrii Kouznetsov's method.
fslog, fsexp for Jay D. Fox's method.

I think there are no objections to this proposal $Wink$