• 0 Vote(s) - 0 Average
• 1
• 2
• 3
• 4
• 5
 Iterated polynomials JmsNxn Long Time Fellow Posts: 571 Threads: 95 Joined: Dec 2010 12/16/2010, 09:00 PM (12/16/2010, 03:00 AM)bo198214 Wrote: (12/14/2010, 03:12 PM)JmsNxn Wrote: I've seen some of you talking about half-iterates of the sin function and I can only guess this is from a general formulae about partial iterates of polynomial functions. the idea is too take half iterates of formal powerseries (not just polynomials). There is a formula for the composition of formal powerseries and you solve then something like $f\circ f = F$, comparing and hence determining the coefficients of the formal powerseries. This works only for $F(0)=0$, i.e. $F$ having a fixed point at 0. In certain cases (e.g. $F'(0)=1$ so called parabolic fixed point at 0, e.g. $e^x-1$ and $\sin(x)$) the resulting powerseries is however not converging. Then you need to take resort in other methods. Perhaps first look at the FAQ, to find in the "General Discussion and Questions". And next take a look at http://mathoverflow.net/questions/4347/f...5227#45227 I also read your other post, it looks very interesting, however for the next weeks I dont have time to dive into. I hope some other forum members reply. Thank you for the link. I said polynomials because I thought there would be a general formula which would extend to power series. I hope someone replies to my other post as well. « Next Oldest | Next Newest »

 Messages In This Thread Iterated polynomials - by JmsNxn - 12/14/2010, 03:12 PM RE: Iterated polynomials - by Gottfried - 12/14/2010, 06:01 PM RE: Iterated polynomials - by JmsNxn - 12/15/2010, 02:40 PM RE: Iterated polynomials - by bo198214 - 12/16/2010, 03:00 AM RE: Iterated polynomials - by JmsNxn - 12/16/2010, 09:00 PM

 Possibly Related Threads... Thread Author Replies Views Last Post Generalized Kneser superfunction trick (the iterated limit definition) MphLee 25 9,145 05/26/2021, 11:55 PM Last Post: MphLee iterated derivation Xorter 0 2,148 06/09/2019, 09:43 PM Last Post: Xorter 1st iterated derivatives and the tetration of 0 Xorter 0 2,964 05/12/2018, 12:34 PM Last Post: Xorter Iterated nand Xorter 2 6,889 03/27/2017, 06:51 PM Last Post: Xorter Bold and Disappointing Experiment With Hermite Polynomials!!! mike3 3 7,826 01/19/2017, 08:05 PM Last Post: JmsNxn Iterated compositions Xorter 0 3,042 08/20/2016, 01:19 PM Last Post: Xorter Grzegorczyk hierarchy vs Iterated differential equations? MphLee 0 3,641 01/03/2015, 11:02 PM Last Post: MphLee Hermite Polynomials mike3 8 16,561 07/08/2014, 12:24 PM Last Post: tommy1729 The fractal nature of iterated ln(x) [Bandwidth warning: lots of images!] jaydfox 16 29,740 09/09/2007, 01:21 AM Last Post: jaydfox Bell formula for iterated exponentiation bo198214 1 6,371 08/26/2007, 12:27 PM Last Post: Gottfried

Users browsing this thread: 1 Guest(s)