However Some functions have a power level of infinity.
And this makes it nontrivial to even decide if this strategy is helpful.
More investigation is neccessary.
Unfortunately i lack time.
For example exp(x) has a power level of infinity.
Exp(x)^a = exp(a x).
The analogue idea of using semi-logarithms instead of sqrt comes to mind.
Another idea is to write
F(x) = exp(a(x)) b(x)
With b(x) growing slower than exp.
Then repeat if necc with a(x) until we get functions a*(x),b(x) that grow slower then exp , and then use the power level tricks on them.
[ this assumes F(x) grows slower then some power tower exp^[k](x). ]
Regards
Tommy1729
And this makes it nontrivial to even decide if this strategy is helpful.
More investigation is neccessary.
Unfortunately i lack time.
For example exp(x) has a power level of infinity.
Exp(x)^a = exp(a x).
The analogue idea of using semi-logarithms instead of sqrt comes to mind.
Another idea is to write
F(x) = exp(a(x)) b(x)
With b(x) growing slower than exp.
Then repeat if necc with a(x) until we get functions a*(x),b(x) that grow slower then exp , and then use the power level tricks on them.
[ this assumes F(x) grows slower then some power tower exp^[k](x). ]
Regards
Tommy1729
