• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Uniqueness of half-iterate of exp(x) ? tommy1729 Ultimate Fellow Posts: 1,372 Threads: 336 Joined: Feb 2009 03/21/2014, 11:55 PM I was dreaming about uniqueness for a half-iterate of exp(x). And what other properties it might have. Let f ( f (x) ) = exp(x) where f (x) and f ' (x) are continu and increasing for all real x. Define L1 as the limit for x -> +oo : L1 = lim L2(x) / (a(x)+b(x)) where a(x) = x + f (x) , b(x) = sqrt(f (x)^2 + x^2) and L2(x) = integral sqrt ( 1 + f ' (x)^2) dx where the integral goes from 0 to x. The conjectured uniqueness is the lowest possible value for L1. Thus let L be the lowest possible value for L1. Then L = L1 and L has a unique function f (x) associated with it. « Next Oldest | Next Newest »

 Messages In This Thread Uniqueness of half-iterate of exp(x) ? - by tommy1729 - 03/21/2014, 11:55 PM RE: Uniqueness of half-iterate of exp(x) ? - by tommy1729 - 03/26/2014, 01:26 PM RE: Uniqueness of half-iterate of exp(x) ? - by tommy1729 - 03/27/2014, 11:23 PM RE: Uniqueness of half-iterate of exp(x) ? - by hixidom - 05/08/2014, 12:57 AM RE: Uniqueness of half-iterate of exp(x) ? - by Gottfried - 05/08/2014, 05:28 AM RE: Uniqueness of half-iterate of exp(x) ? - by hixidom - 05/08/2014, 07:31 AM RE: Uniqueness of half-iterate of exp(x) ? - by Gottfried - 05/08/2014, 01:49 PM RE: Uniqueness of half-iterate of exp(x) ? - by hixidom - 05/08/2014, 04:28 PM RE: Uniqueness of half-iterate of exp(x) ? - by jaydfox - 05/08/2014, 07:04 PM RE: Uniqueness of half-iterate of exp(x) ? - by jaydfox - 05/08/2014, 07:24 PM RE: Uniqueness of half-iterate of exp(x) ? - by hixidom - 05/08/2014, 07:39 PM RE: Uniqueness of half-iterate of exp(x) ? - by Xorter - 01/07/2017, 11:00 PM RE: Uniqueness of half-iterate of exp(x) ? - by Gottfried - 01/08/2017, 01:31 AM RE: Uniqueness of half-iterate of exp(x) ? - by Xorter - 01/08/2017, 10:55 AM RE: Uniqueness of half-iterate of exp(x) ? - by Gottfried - 01/09/2017, 02:41 AM

 Possibly Related Threads... Thread Author Replies Views Last Post Half-iterates and periodic stuff , my mod method [2019] tommy1729 0 1,110 09/09/2019, 10:55 PM Last Post: tommy1729 Approximation to half-iterate by high indexed natural iterates (base on ShlThrb) Gottfried 1 1,634 09/09/2019, 10:50 PM Last Post: tommy1729 Does tetration take the right half plane to itself? JmsNxn 7 9,274 05/16/2017, 08:46 PM Last Post: JmsNxn Half-iteration of x^(n^2) + 1 tommy1729 3 5,802 03/09/2017, 10:02 PM Last Post: Xorter A conjectured uniqueness criteria for analytic tetration Vladimir Reshetnikov 13 16,046 02/17/2017, 05:21 AM Last Post: JmsNxn Removing the branch points in the base: a uniqueness condition? fivexthethird 0 2,166 03/19/2016, 10:44 AM Last Post: fivexthethird [AIS] (alternating) Iteration series: Half-iterate using the AIS? Gottfried 33 51,106 03/27/2015, 11:28 PM Last Post: tommy1729 [2014] Uniqueness of periodic superfunction tommy1729 0 2,558 11/09/2014, 10:20 PM Last Post: tommy1729 irrational iterate of 2z(1-z) BenStandeven 2 5,773 08/09/2014, 10:16 PM Last Post: tommy1729 Real-analytic tetration uniqueness criterion? mike3 25 28,861 06/15/2014, 10:17 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)