• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Taylor polynomial. System of equations for the coefficients. sheldonison Long Time Fellow Posts: 664 Threads: 23 Joined: Oct 2008 05/01/2015, 01:04 PM (05/01/2015, 01:57 AM)marraco Wrote: This is a numerical example for base a=e I had shown how to get 2 sides of a system of equations for solving the coefficients. One side is blue (the linear one), and the other is red (nonlinear, and I still don't know the pattern to generate the complete system of equations. I only got up to x^7, and I can get more, but of course, what I need is a more general expression. ....You might want to compare this to the intuitive slog method. Jay took that farther than anyone else, getting results accurate to 21 decimal digits using his accelerated technique. http://math.eretrandre.org/tetrationforu...php?tid=63 With 8 terms, accuracy is limited to magnitude of the eighth term, and your eighth term is actually larger than Kneser's. If you were able to generate a 20 term approximation, then theoretically, one could have a around 14 decimal digits of accuracy ... assuming the terms scale based on the nearest logarithmic singularity at sexp(-2). For base e, the Taylor's series coefficients of Kneser's solution approach log(x+2) as n gets larger. - Sheldon « Next Oldest | Next Newest »

 Messages In This Thread Taylor polynomial. System of equations for the coefficients. - by marraco - 04/30/2015, 03:24 AM RE: Taylor polinomial. System of equations for the coefficients. - by tommy1729 - 05/01/2015, 08:37 AM RE: Taylor polinomial. System of equations for the coefficients. - by marraco - 05/01/2015, 09:42 AM RE: Taylor polinomial. System of equations for the coefficients. - by tommy1729 - 05/01/2015, 09:43 PM RE: Taylor polinomial. System of equations for the coefficients. - by marraco - 05/03/2015, 04:46 AM RE: Taylor polinomial. System of equations for the coefficients. - by marraco - 05/03/2015, 12:07 PM RE: Taylor polinomial. System of equations for the coefficients. - by Gottfried - 05/05/2015, 07:40 AM RE: Taylor polinomial. System of equations for the coefficients. - by marraco - 05/06/2015, 02:42 PM RE: Taylor polinomial. System of equations for the coefficients. - by Gottfried - 05/06/2015, 04:17 PM RE: Taylor polynomial. System of equations for the coefficients. - by marraco - 05/07/2015, 09:45 AM RE: Taylor polynomial. System of equations for the coefficients. - by marraco - 01/14/2016, 12:47 AM

 Possibly Related Threads... Thread Author Replies Views Last Post Arbitrary Order Transfer Equations JmsNxn 0 309 03/16/2021, 08:45 PM Last Post: JmsNxn New Quantum Algorithms (Carleman linearization) Finally Crack Nonlinear Equations Daniel 2 849 01/10/2021, 12:33 AM Last Post: marraco Moving between Abel's and Schroeder's Functional Equations Daniel 1 2,410 01/16/2020, 10:08 PM Last Post: sheldonison Taylor series of i[x] Xorter 12 20,658 02/20/2018, 09:55 PM Last Post: Xorter Taylor series of cheta Xorter 13 22,573 08/28/2016, 08:52 PM Last Post: sheldonison Totient equations tommy1729 0 3,002 05/08/2015, 11:20 PM Last Post: tommy1729 Bundle equations for bases > 2 tommy1729 0 3,020 04/18/2015, 12:24 PM Last Post: tommy1729 Grzegorczyk hierarchy vs Iterated differential equations? MphLee 0 3,189 01/03/2015, 11:02 PM Last Post: MphLee A system of functional equations for slog(x) ? tommy1729 3 7,310 07/28/2014, 09:16 PM Last Post: tommy1729 partial invariant equations ? tommy1729 0 2,937 03/16/2013, 12:32 AM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)