Thread Rating:
  • 2 Vote(s) - 4 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Searching for an asymptotic to exp[0.5]
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
Reply


Messages In This Thread
RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 09/09/2015, 12:17 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Merged fixpoints of 2 iterates ? Asymptotic ? [2019] tommy1729 1 1,014 09/10/2019, 11:28 AM
Last Post: sheldonison
  Another asymptotic development, similar to 2sinh method JmsNxn 0 2,745 07/05/2011, 06:34 PM
Last Post: JmsNxn



Users browsing this thread: 2 Guest(s)