• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Constructing the "analytical" formula for tetration. mike3 Long Time Fellow Posts: 368 Threads: 44 Joined: Sep 2009 01/28/2011, 03:12 AM (This post was last modified: 01/28/2011, 03:13 AM by mike3.) News: I may have just found a really complicated but "explicit" or "non-recursive" formula for the solutions of a general recurrence sequence of the form $a_1 = r_{1, 1}$, $a_n = \sum_{m=1}^{n-1} r_{n, m} a_m$ which these Schroder function coefficient equations belong to. It's not "nice", though, but it looks to work (no proof yet as it was found by pattern examination). If you want details, just ask. But at least it seems to show that an explicit formula exists, so that there may perhaps be a simpler, more "elegant" one. « Next Oldest | Next Newest »

 Messages In This Thread Constructing the "analytical" formula for tetration. - by mike3 - 01/17/2011, 01:05 PM RE: Constructing the "analytical" formula for tetration. - by Gottfried - 01/17/2011, 10:10 PM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/22/2011, 04:00 AM RE: Constructing the "analytical" formula for tetration. - by Gottfried - 01/24/2011, 08:56 AM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/28/2011, 03:12 AM RE: Constructing the "analytical" formula for tetration. - by Gottfried - 01/28/2011, 02:49 PM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/28/2011, 09:12 PM RE: Constructing the "analytical" formula for tetration. - by Gottfried - 01/28/2011, 10:42 PM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/29/2011, 12:10 AM RE: Constructing the "analytical" formula for tetration. - by mike3 - 02/10/2011, 04:20 AM RE: Constructing the "analytical" formula for tetration. - by sheldonison - 02/10/2011, 05:59 AM RE: Constructing the "analytical" formula for tetration. - by mike3 - 02/10/2011, 07:35 AM RE: Constructing the "analytical" formula for tetration. - by tommy1729 - 01/23/2011, 10:59 PM RE: Constructing the "analytical" formula for tetration. - by mike3 - 01/24/2011, 04:34 AM

 Possibly Related Threads... Thread Author Replies Views Last Post There is a non recursive formula for T(x,k)? marraco 5 3,155 12/26/2020, 11:05 AM Last Post: Gottfried Constructing real tetration solutions Daniel 4 6,165 12/24/2019, 12:10 AM Last Post: sheldonison Recursive formula generating bounded hyper-operators JmsNxn 0 3,341 01/17/2017, 05:10 AM Last Post: JmsNxn Extrapolated Faá Di Bruno's Formula Xorter 1 4,556 11/19/2016, 02:37 PM Last Post: Xorter on constructing hyper operations for bases > eta JmsNxn 1 5,297 04/08/2015, 09:18 PM Last Post: marraco Explicit formula for the tetration to base $$e^{1/e}$$? mike3 1 5,571 02/13/2015, 02:26 PM Last Post: Gottfried Number theoretic formula for hyper operators (-oo, 2] at prime numbers JmsNxn 2 6,902 07/17/2012, 02:12 AM Last Post: JmsNxn fractional iteration by schröder and by binomial-formula Gottfried 0 4,058 11/23/2011, 04:45 PM Last Post: Gottfried simple base conversion formula for tetration JmsNxn 0 4,777 09/22/2011, 07:41 PM Last Post: JmsNxn Change of base formula using logarithmic semi operators JmsNxn 4 12,415 07/08/2011, 08:28 PM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)