Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Rational operators (a {t} b); a,b > e solved
#23
(06/11/2011, 02:33 PM)Gottfried Wrote: Hi James,


Yes this is right:


I did a lot of investigation into this operator (well, to the best that I could).

Quote:and for the h-fold iterated log( 3) then Mike's limit can be expressed

where the operator-precedence is lower the more negative the index at the plus is (so we evaluate it from the left).

First question: is this in fact an application of your "rational operator"?

Well it appears to be. I'm floored, I'm terrible at finding applications.

Quote:And if it is so, then second question: does this help to evaluate this to higher depth of iteration than we can do it when we try it just by log and exp alone (we can do it to iteration 4 or 5 at max I think) ?

Well, not so far since the calculations involved in lower order operators rely on iterations of exp. However, I investigated in seeing if was analytic (which should help in calculations). But I only made it to the sixth or seventh derivative before I realized I wasn't going to recognize the pattern. The thread's here http://www.mymathforum.com/viewtopic.php?f=23&t=20993 .
I assume it would be analytic, (the function looks analytic when graphed, if that's any argument). Also, I think that if is analytic, then is probably analytic, since it's basically the same function with just a faster convergence to y=x and a higher starting point at negative infinity.
Reply


Messages In This Thread
RE: Rational operators (a {t} b); a,b > e solved - by JmsNxn - 06/12/2011, 07:55 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 794 09/09/2019, 10:38 PM
Last Post: tommy1729
  Hyper operators in computability theory JmsNxn 5 4,454 02/15/2017, 10:07 PM
Last Post: MphLee
  Recursive formula generating bounded hyper-operators JmsNxn 0 1,632 01/17/2017, 05:10 AM
Last Post: JmsNxn
  holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 17,400 08/22/2016, 12:19 AM
Last Post: JmsNxn
  The bounded analytic semiHyper-operators JmsNxn 2 3,836 05/27/2016, 04:03 AM
Last Post: JmsNxn
  Bounded Analytic Hyper operators JmsNxn 25 21,518 04/01/2015, 06:09 PM
Last Post: MphLee
  Incredible reduction for Hyper operators JmsNxn 0 2,384 02/13/2014, 06:20 PM
Last Post: JmsNxn
  interpolating the hyper operators JmsNxn 3 5,364 06/07/2013, 09:03 PM
Last Post: JmsNxn
  Number theory and hyper operators JmsNxn 7 8,184 05/29/2013, 09:24 PM
Last Post: MphLee
  Number theoretic formula for hyper operators (-oo, 2] at prime numbers JmsNxn 2 4,208 07/17/2012, 02:12 AM
Last Post: JmsNxn



Users browsing this thread: 1 Guest(s)