Timeline for Monotonicity of the sequences of the lower and upper Darboux sums
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 10, 2017 at 6:08 | comment | added | Włodzimierz Holsztyński | @VictorZurkowski, if you have a counter-example then, please, post it in a separate Answer.. | |
| Apr 6, 2017 at 6:19 | comment | added | Włodzimierz Holsztyński | @AnthonyQuas, I was thinking about sharper integral sums (upper and lower) from the beginning, and I may still do it--first, I was curious at the reception of the present simple version of my question. | |
| Apr 6, 2017 at 1:18 | comment | added | Anthony Quas | The stochastic approach would also apply to $s_n'$ taken to be $s_n'=\sum_{k=1}^n \frac 1{nx+k-\frac 12}$. That should provide a very good lower bound for $\log ((x+1)/x)$. I think the upper bound is much weaker: the error is $O(1/n^2)$. | |
| Apr 5, 2017 at 21:27 | comment | added | Włodzimierz Holsztyński | @AnthonyQuas and VictorZurkowski, reading what you said, how good inequalities does the gets stochastic approach get for the finite harmonic series $\ 1+\frac 12+\frac 13\ldots\ ?$ | |
| Apr 5, 2017 at 19:09 | answer | added | VictorZurkowski | timeline score: 2 | |
| Apr 5, 2017 at 16:03 | answer | added | Anthony Quas | timeline score: 2 | |
| Apr 5, 2017 at 12:57 | comment | added | Anthony Quas | This reminds me of first/second order stochastic dominance, but I haven't yet seen a way to give a proof along those lines. | |
| Apr 5, 2017 at 6:23 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
general case of monotone functions doesn't work, there are easy counterexamples.
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| Apr 4, 2017 at 22:36 | history | edited | Włodzimierz Holsztyński | CC BY-SA 3.0 |
general conjecture
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| Apr 4, 2017 at 22:25 | history | asked | Włodzimierz Holsztyński | CC BY-SA 3.0 |