Thread Rating:
  • 2 Vote(s) - 4 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Searching for an asymptotic to exp[0.5]
#13
Good work guys.
Well perhaps not completely correct but I think going in a good direction.

I have the feeling that you guys are looking for Carlson's theorem.

This creates uniqueness and a newton series.

And by that we switch from the cardinality of functions to that of integers.

Afterthat we can give an integral representation of it.

Ok, maybe Im going to fast now , some more details :

Let a(x) and b(x) be entire functions that are asymptotic to exp^[0.5](x) for x > -1.
Also a(n) = b(n) for integer n.

Since a(n) and b(n) are entire and grow slower than exp , Carlsons theorem applies and

a(x) - b(x) = 0

!!!

So we can make a newton series.

And an integral representation.

And that might help in sheldon's wanted iterated algorithm ... to prove my conjecture for the coefficients.

regards

tommy1729
Reply


Messages In This Thread
RE: Searching for an asymptotic to exp[0.5] - by tommy1729 - 05/12/2014, 11:35 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Merged fixpoints of 2 iterates ? Asymptotic ? [2019] tommy1729 1 586 09/10/2019, 11:28 AM
Last Post: sheldonison
  Another asymptotic development, similar to 2sinh method JmsNxn 0 2,558 07/05/2011, 06:34 PM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)