• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 base holomorphic tetration bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 11/16/2009, 09:01 AM (This post was last modified: 11/16/2009, 09:03 AM by bo198214.) (11/16/2009, 01:10 AM)mike3 Wrote: And what formula are you using for this, the sum one or the limit one? Which requires more numerical precision, esp. near the edge? Mike, I took the extra time to describe it in my previous post: (11/16/2009, 12:30 AM)bo198214 Wrote: I computed the regular iteration as a mixture of the powerseries development at the lower fixed point, together with (if 1 is not inside the convergence radius of this powerseries) the equality $\log_b^{\circ n} \circ \exp_b^{\circ t} \circ \exp_b^{\circ n} = \exp_b^{\circ t}$, i.e. the exponentials move the argument towards the fixed point until it is inside its convergence radius then the powerseries can be applied and the same number of logarithms have to finish the computation. I assumed the convergence radius to be at least the distance of the fixed point from the image of the Shell-Thron region. Quote:What about the vicinity of the area $b = e^{1/e}$? In which form/region you want it to be shown? Different sectors, or decreasing distance to the boundary? « Next Oldest | Next Newest »

 Messages In This Thread base holomorphic tetration - by bo198214 - 11/05/2009, 02:12 PM RE: base holomorphic tetration - by Base-Acid Tetration - 11/05/2009, 10:50 PM RE: base holomorphic tetration - by mike3 - 11/06/2009, 04:15 AM RE: base holomorphic tetration - by mike3 - 11/06/2009, 11:58 AM RE: base holomorphic tetration - by bo198214 - 11/06/2009, 12:12 PM RE: base holomorphic tetration - by mike3 - 11/06/2009, 09:16 PM RE: base holomorphic tetration - by bo198214 - 11/06/2009, 11:29 PM RE: base holomorphic tetration - by mike3 - 11/07/2009, 12:23 AM RE: base holomorphic tetration - by bo198214 - 11/07/2009, 08:17 AM RE: base holomorphic tetration - by mike3 - 11/07/2009, 08:21 AM RE: base holomorphic tetration - by bo198214 - 11/07/2009, 09:55 AM RE: base holomorphic tetration - by bo198214 - 11/07/2009, 04:47 PM RE: base holomorphic tetration - by bo198214 - 11/08/2009, 05:39 PM RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:27 PM RE: base holomorphic tetration - by mike3 - 11/08/2009, 08:25 PM RE: base holomorphic tetration - by bo198214 - 11/08/2009, 08:44 PM RE: base holomorphic tetration - by mike3 - 11/08/2009, 09:51 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Complex Tetration, to base exp(1/e) Ember Edison 7 3,669 08/14/2019, 09:15 AM Last Post: sheldonison Can we get the holomorphic super-root and super-logarithm function? Ember Edison 10 5,865 06/10/2019, 04:29 AM Last Post: Ember Edison Is bounded tetration is analytic in the base argument? JmsNxn 0 1,696 01/02/2017, 06:38 AM Last Post: JmsNxn holomorphic binary operators over naturals; generalized hyper operators JmsNxn 15 18,937 08/22/2016, 12:19 AM Last Post: JmsNxn tetration base sqrt(e) tommy1729 2 3,917 02/14/2015, 12:36 AM Last Post: tommy1729 Explicit formula for the tetration to base [tex]e^{1/e}[/tex]? mike3 1 3,479 02/13/2015, 02:26 PM Last Post: Gottfried tetration base > exp(2/5) tommy1729 2 3,678 02/11/2015, 12:29 AM Last Post: tommy1729 regular tetration base sqrt(2) : an interesting(?) constant 2.76432104 Gottfried 7 10,753 06/25/2013, 01:37 PM Last Post: sheldonison tetration base conversion, and sexp/slog limit equations sheldonison 44 63,325 02/27/2013, 07:05 PM Last Post: sheldonison simple base conversion formula for tetration JmsNxn 0 3,589 09/22/2011, 07:41 PM Last Post: JmsNxn

Users browsing this thread: 1 Guest(s)