• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 matrix function like iteration without power series expansion Gottfried Ultimate Fellow Posts: 758 Threads: 117 Joined: Aug 2007 07/02/2008, 11:23 AM (This post was last modified: 07/02/2008, 11:25 AM by Gottfried.) bo198214 Wrote:Guys! That I didnt see that before! We have a very simple formula for computing the $t$-th iterate of an arbitrary function: $f^{\circ t} = \sum_{n=0}^\infty \left(t\\n\right) \sum_{k=0}^n \left(n\\k\right) (-1)^{n-k} f^{\circ k}$ I want to add, that this expression exites me very much. Just these days I was looking for alternatives (hopefully improvements) of our fractional iteration problem. I was looking for two aspects expression of the tetration by its own powertowers instead of powerseries interpolation not done based on polynomial interpolation of the coefficients of the powerseries but based on an interpolation of gamma The above formula provides both searched aspects in one shot. The first is obvious; the idea is that only values are involved, which are provided by the function itself (so, for instance, possibly only of a relevant subset of complex numbers which are accessible by the function and its iterates itself/themselves - hmm, amateurish expressed; I hope the idea behind this can be understood anyway) The second, because the fractional binomials use gamma of fractional parameters. So - in my view - this is a big shot... Gottfried Gottfried Helms, Kassel « Next Oldest | Next Newest »

 Messages In This Thread matrix function like iteration without power series expansion - by bo198214 - 06/30/2008, 03:01 PM RE: matrix function like iteration without power series expansion - by Gottfried - 06/30/2008, 09:23 PM RE: matrix function like iteration without power series expansion - by bo198214 - 07/01/2008, 06:48 AM RE: matrix function like iteration without power series expansion - by Gottfried - 07/01/2008, 02:18 PM RE: matrix function like iteration without power series expansion - by Gottfried - 07/02/2008, 11:23 AM RE: matrix function like iteration without power series expansion - by Gottfried - 07/08/2008, 06:56 AM RE: matrix function like iteration without power series expansion - by andydude - 07/08/2008, 06:01 PM RE: matrix function like iteration without power series expansion - by andydude - 07/08/2008, 09:35 PM RE: matrix function like iteration without power series expansion - by Gottfried - 07/08/2008, 06:23 PM RE: matrix function like iteration without power series expansion - by Gottfried - 07/09/2008, 08:58 AM RE: matrix function like iteration without power series expansion - by andydude - 07/09/2008, 02:38 PM RE: matrix function like iteration without power series expansion - by andydude - 07/09/2008, 02:57 PM RE: matrix function like iteration without power series expansion - by bo198214 - 07/09/2008, 06:18 PM RE: matrix function like iteration without power series expansion - by andydude - 07/14/2008, 06:21 PM RE: matrix function like iteration without power series expansion - by bo198214 - 07/14/2008, 09:55 PM RE: matrix function like iteration without power series expansion - by Gottfried - 07/10/2008, 07:01 AM

 Possibly Related Threads... Thread Author Replies Views Last Post New mathematical object - hyperanalytic function arybnikov 4 200 01/02/2020, 01:38 AM Last Post: arybnikov Perhaps a new series for log^0.5(x) Gottfried 0 165 12/05/2019, 04:35 PM Last Post: Gottfried Is there a function space for tetration? Chenjesu 0 438 06/23/2019, 08:24 PM Last Post: Chenjesu A Notation Question (raising the highest value in pow-tower to a different power) Micah 8 2,658 02/18/2019, 10:34 PM Last Post: Micah Degamma function Xorter 0 885 10/22/2018, 11:29 AM Last Post: Xorter Taylor series of i[x] Xorter 12 11,733 02/20/2018, 09:55 PM Last Post: Xorter Functional power Xorter 0 1,324 03/11/2017, 10:22 AM Last Post: Xorter Complaining about MSE ; attitude against tetration and iteration series ! tommy1729 0 1,621 12/26/2016, 03:01 AM Last Post: tommy1729 2 fixpoints , 1 period --> method of iteration series tommy1729 0 1,480 12/21/2016, 01:27 PM Last Post: tommy1729 2 fixpoints related by power ? tommy1729 0 1,463 12/07/2016, 01:29 PM Last Post: tommy1729

Users browsing this thread: 1 Guest(s)