Timeline for Computing infinite series with iterated functions
Current License: CC BY-SA 4.0
15 events
| when toggle format | what | by | license | comment | |
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| Jun 25, 2021 at 7:18 | comment | added | Lutz Lehmann | On the function sequence involved, the iterated sine, or any other of the form $y_{k+1}=y_k-ay_k^3+...$, see math.stackexchange.com/questions/1449281/…, math.stackexchange.com/questions/1609995/…, math.stackexchange.com/questions/105452/… | |
| Jun 23, 2021 at 15:09 | vote | accept | Ryan Howe | ||
| S Jun 22, 2021 at 20:28 | history | suggested | Tyberius | CC BY-SA 4.0 |
added python script identifier
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| Jun 22, 2021 at 20:16 | review | Suggested edits | |||
| S Jun 22, 2021 at 20:28 | |||||
| Jun 22, 2021 at 5:53 | answer | added | Abdullah Ali Sivas | timeline score: 4 | |
| Jun 22, 2021 at 3:01 | answer | added | Maxim Umansky | timeline score: 4 | |
| Jun 22, 2021 at 2:46 | comment | added | Maxim Umansky | I don't believe there is a finite limit here because for each term the integral $\int_0^{\pi} f_n(x) dx > \int_0^{\epsilon} f_n(x) dx$, for any positive $\epsilon < \pi$. So if we take $\epsilon \ll 1$ then $f_n(x) \to x$ and the sum becomes $\sum_1^n \epsilon^2/2 = n \epsilon^2/2$ which diverges for $n \to \infty$. | |
| Jun 22, 2021 at 0:26 | comment | added | Ryan Howe | Ahh, that's probably a better idea. Thank you. | |
| Jun 22, 2021 at 0:20 | comment | added | nicoguaro♦ | I didn't used a recursive function. I stored the last two values and accumulated them. | |
| Jun 22, 2021 at 0:18 | comment | added | Ryan Howe | I'm not sure. I hit the max recursion depth and it was slow with Python when writing it quickly. The terms appear to get smaller but very slowly and I originally just terminate where the difference between the nth partial sum and n+1 partial sum was smaller than a given tolerance (like 0.01) as then the terms would only be increasing by 1 every hundred iterations. | |
| Jun 22, 2021 at 0:03 | comment | added | nicoguaro♦ | Sorry, I meant "the sequence formed by the partial sums". I tried with 1000 000 terms. I think that sequence gives an estimate for a lower bound since you can come the area of the triangle that lies below your convex function as $f_{\max} \pi/2$. | |
| Jun 21, 2021 at 23:55 | comment | added | Ryan Howe | It seemed to be decreasing monotonically. Here are the first 250 values (gist.github.com/Shogun89/b32b6eec46e59349cb8fcbaf6b9b2113). As you can see it's already beneath 1 by n=17 and beneath 0.5 at n=93. | |
| Jun 21, 2021 at 23:25 | comment | added | nicoguaro♦ | Are you sure it converges? I appears that sequence formed by the function evaluated at $\pi/2$ (the maximum of the function) grows monotonically. | |
| Jun 21, 2021 at 23:01 | review | First posts | |||
| Jun 22, 2021 at 13:25 | |||||
| Jun 21, 2021 at 22:57 | history | asked | Ryan Howe | CC BY-SA 4.0 |