05/05/2022, 11:03 PM
(05/04/2022, 10:31 PM)JmsNxn Wrote:(05/03/2022, 12:16 PM)tommy1729 Wrote:(03/23/2022, 03:19 AM)JmsNxn Wrote: Hey everyone! Some more info dumps!
I haven't talked too much about holomorphic semi-operators for a long time. For this brief exposition I'm going to denote the following:
\[
\begin{align}
x\,<0>\,y &= x+y\\
x\,<1>\,y &= x\cdot y\\
x\,<2>\,y &= x^y\\
\end{align}
\]
Where we have the identity: \(x<k>(x<k+1>y) = x<k+1> y+1\). Good ol fashioned hyper-operators.
...
First note :
In my notebook - and maybe posted here too - i found the identity: \((x<k+1>y) <k>x= x<k+1> y+1\) is consistant with
\[
\begin{align}
x\,<0>\,y &= x+y\\
x\,<1>\,y &= x\cdot y\\
x\,<2>\,y &= x^y\\
\end{align}
\]
This seems a nicer choice or not ?
Why not this ? because it is slower ?
Second note : Im going to ignore holomorphic for now because I do not believe that. Might explain later ( more time ) and maybe already did in the past.
Third note :
Which fractional iteration for exp and log ?? There are many and they do not agree on the 2 real fixpoints or ( in case of base e^(1/e) a single real fixpoint that is not analytic ! )
These problems and choices are not simultaniously adressed , picked and motivated.
Fourth note : why non-commutative ?
Fifth note :
you basicly are looking for a function f_1(a,b,s) and " find " the solution f_2(a ,b ,s , f_3(a,b,s) ) where f_3(a,b,s ) is unknown , undefined and unproven analytic.
that feels like solving the quintic polynomial as exp(a_0) + f(a_0,a_2,a_3,a_4,a_5) for some unknown f ...
forgive my parody.
I could continue but I respect you
regards
tommy1729
1) I don't want left associative, who wants left associative....
...
Like I commented , your original equation mentioned IS left associative.