Timeline for Asymptotics of the derivatives of analytic functions
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 8, 2015 at 2:26 | vote | accept | Iosif Pinelis | ||
| Nov 8, 2015 at 2:25 | comment | added | Iosif Pinelis | Thank you Michael for another nice comment. I had indeed tried to bound $f^{(k)}(x)$ for "my" particular function $f$ of interest by showing that $|f(z)|=O(|z|+1)$ for $z$ in an open sector containing $(0,\infty)\subset\mathbb{R}$, but have succeeded only now in that. | |
| Nov 6, 2015 at 7:50 | comment | added | Michael Renardy | If the asymptotics applies in a sector rather than just the real axis, you can use Cauchy's formula for derivatives. | |
| Nov 6, 2015 at 4:47 | comment | added | Iosif Pinelis | Thank you Michael for the nice point. I admit that my question was not sufficiently well thought out; sorry. Pietro's reference to Carleman's result is quite educational to me. Still, is there a way to answer the more general question posed above: What additional conditions are needed to ensure the desired asymptotics? | |
| Nov 5, 2015 at 23:04 | answer | added | Mark Fischler | timeline score: 0 | |
| Nov 5, 2015 at 23:00 | comment | added | Michael Renardy | Consider what happens, for instance, if you change $f(z)$ to $f(z)+z^{-2}\cos({\pi/2}(e^z-z))$. | |
| Nov 5, 2015 at 22:58 | answer | added | Pietro Majer | timeline score: 3 | |
| Nov 5, 2015 at 22:35 | history | edited | Iosif Pinelis | CC BY-SA 3.0 |
added 12 characters in body
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| Nov 5, 2015 at 22:27 | history | asked | Iosif Pinelis | CC BY-SA 3.0 |