Holomorphic semi operators, using the beta method

[tommy1729]

Alright!

For fucks sakes. I got by by the skin of my teeth. I have an analytic solution. It's going to be a while to get it coherent and make a write up well enough. I got super fucking lucky though. The infinite composition needed to solve this first order difference equation converges like:

\[
\sum \frac{1}{n\log(n)^2}\\
\]

Which, is like the slowest possible convergence. So don't expect an efficient algorithm as of yet. But I can derive an analytic solution because thank the fuck that it wasn't \(\frac{1}{n\log(n)}\) which diverges.

So the solution I can construct analytically converges, but it's as slow as fucking possible -_-.

Well apart from not knowing what you have discovered :

\[
\sum \frac{1}{n\log(n) (log(log(n))^2}\\
\]

Is much slower.
And you can keep getting slower by adding log iterations.
And after that slog stuff.

But perhaps you meant slowest with 1 log.

anyway

Let f(x,s,y) be a hyperoperator or at least an analytic function or a continu function for some intervals in x , s , y.

Then how do you feel about the set of equations : 

f(x , s-1 , f(x , s , y)) = f(x , s, f(y , s-1 , 1))
f(x , s , f(y , s-1 , z)) = f(f(x , s , y) , s-1 , f(x , s , z))

or in tex :

\[f(x , s-1 , f(x , s , y)) = f(x , s, f(y , s-1 , 1))\]
\[f(x , s , f(y , s-1 , z)) = f(f(x , s , y) , s-1 , f(x , s , z))\]

solved simultan.

Does this work out ?

Uniqueness ?
 

Sorry if i change things a bit again.

regards

tommy1729