Timeline for On the continuity of $\sum_{n=1}^{\infty} \sin(nx) / n^\alpha$
Current License: CC BY-SA 4.0
5 events
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Nov 28, 2021 at 18:29 | comment | added | Dmitry Krachun | @username well, here we pair summands with indices $n$ and $n+k$, so these are at bounded distance, which is fine | |
Nov 27, 2021 at 22:27 | comment | added | username | My concern is that reordering the order of summation in a semi-convergent series can lead to anything (to any positive of negative real as you know). Can you say a word about why this particular reordering does not change the sum? | |
Nov 27, 2021 at 21:50 | comment | added | Fedor Petrov | @username by partitioning the terms onto pairs as described | |
Nov 27, 2021 at 18:32 | comment | added | username | How do you bound the rest of the sum, $\sum_{2k+1}^\infty \sin\left(\pi \frac nk\right) \frac{1}{n^\alpha}$? | |
Nov 27, 2021 at 16:26 | history | answered | Dmitry Krachun | CC BY-SA 4.0 |