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 Nowhere analytic superexponential convergence bo198214 Administrator Posts: 1,389 Threads: 90 Joined: Aug 2007 01/29/2011, 11:53 PM (This post was last modified: 01/29/2011, 11:55 PM by bo198214.) (01/29/2011, 08:59 PM)tommy1729 Wrote: well according to Bo it is not real-analytic and it doesnt have a radius , and according to mike it does have a radius. I was not talking about $\log^{[n]}(\exp^{[n]}(x))$ which is for each $n$ the identity function. Of course it is real-analytic, even entire. I was talking about tommysexp construction and the basechange. In each step it has a radius of convergence, which though diminishes to 0 for $n\to\infty$. Quote:so opinions and/or terminology differs They dont. Quote: , i hope at least everyone agrees on : on the real line f(x) = lim n -> oo log^[n] ( exp^[n] (x) ) is real-analytic because it simply reduces to f(x) = x for real x , which is clearly real-analytic. Of course. Quote:and for real-analytic i prefer to say : analytic on an interval , rather than a radius , for imho a nonzero-radius is for analytic taylor series - analytic on on a disk on the complex plane with nonzero-radius. "analytic" is defined for a point (in a neighborhood, so one can take derivatives). If one says "analytic on an interval", it means "for each point on the interval". If one says "analytic on a disk", it means "for each point of the disk". However "analytic at a point" always implies being analytic on the open disk of convergence, i.e. being analytic at each point of the disk of convergence. I hope this brings some light into your confusion « Next Oldest | Next Newest »

 Messages In This Thread Nowhere analytic superexponential convergence - by sheldonison - 01/20/2011, 05:23 PM RE: Nowhere analytic superexponential convergence - by tommy1729 - 01/21/2011, 12:21 AM RE: Nowhere analytic superexponential convergence - by sheldonison - 01/26/2011, 12:49 AM RE: Nowhere analytic superexponential convergence - by tommy1729 - 01/26/2011, 11:17 PM RE: Nowhere analytic superexponential convergence - by bo198214 - 01/28/2011, 11:29 PM RE: Nowhere analytic superexponential convergence - by tommy1729 - 01/29/2011, 12:03 AM RE: Nowhere analytic superexponential convergence - by bo198214 - 01/29/2011, 10:21 AM RE: Nowhere analytic superexponential convergence - by tommy1729 - 01/29/2011, 03:26 PM RE: Nowhere analytic superexponential convergence - by mike3 - 01/29/2011, 08:41 PM RE: Nowhere analytic superexponential convergence - by tommy1729 - 01/29/2011, 08:59 PM RE: Nowhere analytic superexponential convergence - by bo198214 - 01/29/2011, 11:53 PM RE: Nowhere analytic superexponential convergence - by tommy1729 - 01/30/2011, 06:48 PM RE: Nowhere analytic superexponential convergence - by bo198214 - 01/31/2011, 04:00 AM RE: Nowhere analytic superexponential convergence - by sheldonison - 01/31/2011, 04:47 AM RE: Nowhere analytic superexponential convergence - by sheldonison - 02/10/2011, 07:22 AM

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