Timeline for non-analytic functions with arbitrary large derivatives [closed]
Current License: CC BY-SA 3.0
11 events
| when toggle format | what | by | license | comment | |
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| Apr 19, 2018 at 16:00 | comment | added | Willie Wong | @fedja: thank you. (That's a great qualifying exam question.) | |
| Apr 19, 2018 at 15:12 | history | closed |
Andrés E. Caicedo Alexandre Eremenko coudy David Handelman Michael Renardy |
Not suitable for this site | |
| Apr 19, 2018 at 14:45 | comment | added | fedja | @WillieWong $f(1)=\sum_{k=0}^n \frac{f^{(k)}(0)}{k!}+\frac{f^{(n+1)}(\xi)}{(n+1)!}\ge\sum_{k=0}^n \frac{a_k}{k!}$ for every $n$, so if the series $\sum_k\frac{a_k}{k!}$ diverges, you are in trouble. | |
| Apr 19, 2018 at 13:49 | history | edited | Ali | CC BY-SA 3.0 |
edited body
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| Apr 19, 2018 at 13:45 | comment | added | Willie Wong | @fedja: I am feeling dense. I don't quite understand your comment. Can you elaborate a little bit more? | |
| Apr 19, 2018 at 13:43 | comment | added | Willie Wong | Your comment is not the same as what you asked in the question. Your question asks for the $\sup$ to be lower bounded, for that you just need one point. Your comment asks for every point. Did you want $\inf$? | |
| Apr 19, 2018 at 11:39 | review | Close votes | |||
| Apr 19, 2018 at 15:15 | |||||
| Apr 19, 2018 at 11:35 | comment | added | fedja | Over all interval obviously not always. Just estimate $f(1)$ using Taylor formula at $0$ of high order. | |
| Apr 19, 2018 at 11:28 | comment | added | Ali | the only difference is that here I want the bounds to hold over all the interval where as in Borel's lemma it holds only at one point of the interval. perhaps there is a simple way to extend the result? | |
| Apr 19, 2018 at 11:16 | comment | added | abx | Yes, see Borel's lemma. | |
| Apr 19, 2018 at 11:11 | history | asked | Ali | CC BY-SA 3.0 |