• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Infinite Pentation (and x-srt-x) bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 05/31/2011, 10:29 PM (This post was last modified: 05/31/2011, 10:31 PM by bo198214.) (04/11/2009, 09:16 AM)andydude Wrote: If we interpolate these points, one would except the interpolation to diverge for infinite pentation, and x-superroot-x, but the interpolating polynomial of these integer points do seem to converge, Now I doubt about the interpolation method. If the interpolation of the self-tetra-root would yield a valid function, then shoud the interpolation of the simple self-root $n^{1/n}$ also converge to the self-root $x^{1/x}$ on $x>0$. But this seems not to be the case. An interpolation polynomial of degree 400 (401 sample points) still has a negative value at 0.25.     And if we compare the values it seems that the negativity gets rather worse: 101 points: $f(0.25)\approx -0.235$ 201 points: $f(0.25)\approx -0.330$ 301 points: $f(0.25)\approx -0.364$ 401 points: $f(0.25)\approx -0.378$ So it really looks as if the interpolation (even if it converges) does not converge to $x^{1/x}$ which is positive everywhere. So I would conclude that the interpolation of the self-tetra-root also does not converge to a self-tetra-root, even if it converges. « Next Oldest | Next Newest »

 Messages In This Thread Infinite Pentation (and x-srt-x) - by andydude - 04/11/2009, 09:16 AM RE: Infinite Pentation (and x-srt-x) - by bo198214 - 04/11/2009, 09:31 AM RE: Infinite Pentation (and x-srt-x) - by andydude - 04/11/2009, 07:54 PM RE: Infinite Pentation (and x-srt-x) - by nuninho1980 - 04/11/2009, 12:44 PM RE: Infinite Pentation (and x-srt-x) - by andydude - 04/11/2009, 06:42 PM RE: Infinite Pentation (and x-srt-x) - by nuninho1980 - 04/11/2009, 01:24 PM RE: Infinite Pentation (and x-srt-x) - by andydude - 04/11/2009, 06:30 PM RE: Infinite Pentation (and x-srt-x) - by andydude - 04/11/2009, 06:50 PM RE: Infinite Pentation (and x-srt-x) - by nuninho1980 - 04/11/2009, 09:58 PM RE: Infinite Pentation (and x-srt-x) - by andydude - 04/12/2009, 08:19 AM RE: Infinite Pentation (and x-srt-x) - by andydude - 04/11/2009, 08:11 PM RE: Infinite Pentation (and x-srt-x) - by andydude - 04/12/2009, 08:58 AM RE: Infinite Pentation (and x-srt-x) - by bo198214 - 04/13/2009, 05:01 PM RE: Infinite Pentation (and x-srt-x) - by tommy1729 - 05/03/2009, 10:42 PM RE: Infinite Pentation (and x-srt-x) - by bo198214 - 05/03/2009, 10:51 PM RE: Infinite Pentation (and x-srt-x) - by tommy1729 - 05/03/2009, 10:57 PM RE: Infinite Pentation (and x-srt-x) - by bo198214 - 05/03/2009, 11:20 PM RE: Infinite Pentation (and x-srt-x) - by BenStandeven - 05/04/2009, 08:20 PM RE: Infinite Pentation (and x-srt-x) - by bo198214 - 05/04/2009, 08:57 PM RE: Infinite Pentation (and x-srt-x) - by andydude - 04/13/2009, 05:27 AM RE: Infinite Pentation (and x-srt-x) - by bo198214 - 05/31/2011, 10:29 PM

 Possibly Related Threads... Thread Author Replies Views Last Post pentation and hexation sheldonison 9 9,841 09/18/2019, 02:34 PM Last Post: sheldonison [repost] A nowhere analytic infinite sum for tetration. tommy1729 0 1,430 03/20/2018, 12:16 AM Last Post: tommy1729 Tetration is pentation. This deserve more thinking. marraco 2 3,930 03/30/2015, 02:54 PM Last Post: marraco [2015] 4th Zeration from base change pentation tommy1729 5 6,522 03/29/2015, 05:47 PM Last Post: tommy1729 Mizugadro, pentation, Book Kouznetsov 41 51,409 03/02/2015, 08:13 PM Last Post: sheldonison [MO] Is there a tetration for infinite cardinalities? (Question in MO) Gottfried 10 13,242 12/28/2014, 10:22 PM Last Post: MphLee Remark on Gottfried's "problem with an infinite product" power tower variation tommy1729 4 5,642 05/06/2014, 09:47 PM Last Post: tommy1729 Problem with infinite product of a function: exp(x) = x * f(x)*f(f(x))*... Gottfried 5 7,546 07/17/2013, 09:46 AM Last Post: Gottfried Wonderful new form of infinite series; easy solve tetration JmsNxn 1 4,674 09/06/2012, 02:01 AM Last Post: JmsNxn the infinite operator, is there any research into this? JmsNxn 2 5,860 07/15/2011, 02:23 AM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)