Timeline for Asymptotics of a Bernoulli-number-like function
Current License: CC BY-SA 4.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 1, 2021 at 21:55 | history | edited | Timothy Chow | CC BY-SA 4.0 |
Added references
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| Nov 27, 2011 at 2:19 | comment | added | Noam D. Elkies | Steve Huntsman's .721 is correct as far as it goes, but you get only one more decimal place before the oscillation about $1 / \log 4$ sets in. The guess $$(2k-2)/(2k-1) = 1 - 1/2k - 1/4k^2 - 1/8k^3 - \cdots$$ is correct only through the $k^{-1}$ term; the correct expansion (any partial sum of which is elementary) is $$1 - 1/2k - 1/12k^2 - 1/24k^3 - 19/720k^4 - \cdots.$$ See my answer below for more. | |
| Nov 26, 2011 at 19:19 | vote | accept | Timothy Chow | ||
| Nov 12, 2011 at 4:09 | answer | added | Noam D. Elkies | timeline score: 18 | |
| Jun 28, 2010 at 10:47 | comment | added | Wadim Zudilin | Timothy, your question looks very close to the asymptotics I want as well (mathoverflow.net/questions/25661 although I give a link rather than the full derivation). Could your/Tony's problem be related to the Erd\H{o}s name?! | |
| Jan 10, 2010 at 13:40 | answer | added | Tony Lezard | timeline score: 4 | |
| Jan 10, 2010 at 1:05 | answer | added | Douglas Zare | timeline score: 4 | |
| Jan 10, 2010 at 0:28 | answer | added | Reid Barton | timeline score: 8 | |
| Jan 9, 2010 at 23:18 | answer | added | Michael Lugo | timeline score: 10 | |
| Jan 9, 2010 at 23:01 | comment | added | Steve Huntsman | Also it looks like for $k$ large that $\lim_n f(n,k) \approx \frac{2k-2}{2k-1}$. | |
| Jan 9, 2010 at 21:55 | comment | added | Steve Huntsman | MATLAB suggests that $\lim_{n \uparrow \infty} f(n,2) \approx 0.721$. | |
| Jan 9, 2010 at 21:37 | history | asked | Timothy Chow | CC BY-SA 2.5 |