Timeline for Convergence of an inverted Fourier series
Current License: CC BY-SA 4.0
3 events
| when toggle format | what | by | license | comment | |
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| Nov 13 at 9:29 | comment | added | Julien Marché | Thanks Conrad for your answer, I did not know about the Flint Hills problem. Any other comments on the properties of this function are welcome. | |
| Nov 12 at 16:26 | comment | added | Conrad | this stuff is related to the irrationality measure of $x$ - it is easy to construct numbers for which $|x-p_m/q_m| << q_m^{-4}$ for example for infinitely many $m$ and some (distinct) fractions $p_m/q_m$ and then $|\pi q_mx-\pi p_m| << q_m^{-3}$ so $1/q_m^3\sin q_m \pi x$ doesn't converge to $0$ and the series perforce diverges etc; for $x=1/\pi$ this is related to the well known Flint Hills problem and the irrationality measure of $\pi$ | |
| Nov 12 at 16:08 | history | asked | Julien Marché | CC BY-SA 4.0 |