10/19/2016, 08:47 AM

So originally i tried to work from " the inside " like but from " the outside " like we got already the following result.

( i Will omit x sometimes , since it Goes to oo )

For

Now z > 1 must be true.

Simplify

Since z > 1 and we get

and

.

--

Notice for integer n > 0 we get by the above and induction

~~

I assume it holds for n = 0 , that would imply that powers dominate bases for subexponential tetration.

In other words

Conjecture for p > 1 :

--

However we need much better understanding and approximations.

We are not close to answering

semiexp_q * semiexp_s ~ semiexp_d ^ R

For a given pair (q,s) and a desired best fit (d,R).

I considered the base change but without succes. The approximation slog - slog_b ~~ constant is insufficient.

See also

http://math.stackexchange.com/questions/...ase-a-e1-e

Although that might be hard to read.

Regards

Tommy1729

( i Will omit x sometimes , since it Goes to oo )

For

Now z > 1 must be true.

Simplify

Since z > 1 and we get

and

.

--

Notice for integer n > 0 we get by the above and induction

~~

I assume it holds for n = 0 , that would imply that powers dominate bases for subexponential tetration.

In other words

Conjecture for p > 1 :

--

However we need much better understanding and approximations.

We are not close to answering

semiexp_q * semiexp_s ~ semiexp_d ^ R

For a given pair (q,s) and a desired best fit (d,R).

I considered the base change but without succes. The approximation slog - slog_b ~~ constant is insufficient.

See also

http://math.stackexchange.com/questions/...ase-a-e1-e

Although that might be hard to read.

Regards

Tommy1729