Timeline for How to create a function whose harmonic is a sine wave
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 17, 2019 at 10:18 | comment | added | Gerald Edgar | Of course, this is only one solution. There could be additional solutions where $f(n^k x)/n^k$ does not converge to $0$. | |
| May 17, 2019 at 1:22 | comment | added | mrplants | Okay, walked through it on paper and just have a small edit: the answer is actually $\sum_{k=0}^\infty\left(\frac{1}{n}\right)^k\sin(n^kx)$ | |
| May 17, 2019 at 0:58 | comment | added | mrplants | Does this function have a name or any special properties? Anywhere I can learn more about this? | |
| May 17, 2019 at 0:54 | vote | accept | mrplants | ||
| May 17, 2019 at 0:54 | comment | added | mrplants | That's amazing. Thank you. | |
| May 17, 2019 at 0:38 | comment | added | Nick S | @mrplants $$f(x)+\frac{1}{n}f(nx)=\sin(x)\\ \frac{1}{n}f(nx)+\frac{1}{n^2}f(n^2x)=\frac{1}{n}\sin(nx) \\\frac{1}{n^2}f(n^2x)+\frac{1}{n^3}f(n^3x)=\frac{1}{n^2} \sin(x) \\\...$$Now, first equation minus second plus third and so on... | |
| May 17, 2019 at 0:33 | comment | added | mrplants | Can you provide details on how to solve this or point me to somewhere with more information? I'd like to learn more. | |
| May 17, 2019 at 0:26 | history | answered | Michael Renardy | CC BY-SA 4.0 |