• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Comparing the Known Tetration Solutions bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 08/17/2007, 11:45 PM (This post was last modified: 08/17/2007, 11:48 PM by bo198214.) andydude Wrote:If by my solution you mean ${\ }^{y}(e^{1/e})$ through parabolic iteration of $e^x-1$No, I meant the piecewise infinite differentiable definition of slog. Isnt it defined for arbirtrary bases? (I think you wrote for base greater 1.) So if you have the slog you have also the "sexp". And I would compare this with what comes out from Daniel's solution for the hyperbolic case (there is then no problem with the convergence radius of the series). Quote:and by Daniel's you mean ${\ }^{y}(b^{1/b})$ through hyperbolic iteration of $b^x-1$ Rather $b^x-x_0$, i.e. to develop $b^x$ at the (lower) fixed point $b^{x_0}=x_0$ which is given (if I remember correctly) by $x_0=\frac{W(-\log(b))}{-\log(b)}$ and then take hyperbolic iterations ${}^xb=\exp^{\circ x}_b(1.0)$. « Next Oldest | Next Newest »

 Messages In This Thread Comparing the Known Tetration Solutions - by bo198214 - 08/17/2007, 09:13 PM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/20/2007, 09:59 AM RE: Comparing the Known Tetration Solutions - by bo198214 - 08/20/2007, 11:09 AM New pictures from the hyperbolic slog! - by bo198214 - 08/20/2007, 01:36 PM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/20/2007, 05:35 PM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/21/2007, 05:06 AM RE: Comparing the Known Tetration Solutions - by andydude - 08/22/2007, 11:28 PM RE: Comparing the Known Tetration Solutions - by bo198214 - 08/23/2007, 12:14 AM RE: Comparing the Known Tetration Solutions - by Gottfried - 08/29/2007, 06:19 AM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/29/2007, 06:15 PM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/29/2007, 12:06 AM RE: Comparing the Known Tetration Solutions - by jaydfox - 08/29/2007, 01:56 AM RE: Comparing the Known Tetration Solutions - by bo198214 - 08/29/2007, 07:48 AM RE: Comparing the Known Tetration Solutions - by andydude - 08/29/2007, 08:19 AM RE: computing the iterated exp(x)-1 - by andydude - 08/17/2007, 11:20 PM RE: computing the iterated exp(x)-1 - by jaydfox - 08/17/2007, 11:38 PM RE: computing the iterated exp(x)-1 - by bo198214 - 08/17/2007, 11:45 PM RE: computing the iterated exp(x)-1 - by jaydfox - 08/18/2007, 12:19 AM RE: computing the iterated exp(x)-1 - by bo198214 - 08/18/2007, 08:19 AM RE: computing the iterated exp(x)-1 - by andydude - 08/18/2007, 09:35 AM RE: computing the iterated exp(x)-1 - by bo198214 - 08/18/2007, 11:59 AM RE: computing the iterated exp(x)-1 - by jaydfox - 08/18/2007, 03:49 PM RE: computing the iterated exp(x)-1 - by jaydfox - 08/19/2007, 12:50 AM RE: Comparing the Known Tetration Solutions - by bo198214 - 08/19/2007, 10:55 AM

 Possibly Related Threads... Thread Author Replies Views Last Post Constructing real tetration solutions Daniel 4 1,182 12/24/2019, 12:10 AM Last Post: sheldonison Solutions to f ' (x) = f(f(x)) ? tommy1729 1 2,603 08/12/2013, 12:10 AM Last Post: tommy1729 Imaginary zeros of f(z)= z^(1/z) (real valued solutions f(z)>e^(1/e)) Gottfried 91 102,170 03/03/2011, 03:16 PM Last Post: Gottfried Infinite towers & solutions to Lambert W-function brangelito 1 4,170 06/16/2010, 02:50 PM Last Post: bo198214

Users browsing this thread: 1 Guest(s)