03/11/2017, 10:22 AM
Let f and g be total functions (so e. g. C -> C) and N and M be complexes.
Then (f o g)(x) and f o a = f(a) are so-called functional multiplications. But the interesting thing is the following: functional power:
)
When N is an integer, it is trivial, just look:
...
We have rules for it, like these ones:
 o (f^{oM}) = f^{o N+ M})
^{oM} = f^{o N M})
 = (f^{oN}) o f = f^{o N+1})
But for instance:
 o (g)^{oN} != (f o g)^{oN})
(Also functional tetration exists.)
My theory is that if we can get an explicit formula for
with x and N, then N is extendable to any total function.
For example:
^{oN} = 2^N x<br />
N := log_2 (x)<br />
(2x)^{o log_2 (x)} = x^2)
And in the same way, theoritacelly you could do the same with all the functions.
But how?
My concept is that by Carleman matrices.
Then (f o g)(x) and f o a = f(a) are so-called functional multiplications. But the interesting thing is the following: functional power:
When N is an integer, it is trivial, just look:
...
We have rules for it, like these ones:
But for instance:
(Also functional tetration exists.)
My theory is that if we can get an explicit formula for
For example:
And in the same way, theoritacelly you could do the same with all the functions.
But how?
My concept is that by Carleman matrices.
Xorter Unizo
