Timeline for Questions about iterating the Euler-Maclaurin summation formula
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 6, 2022 at 19:11 | comment | added | François Brunault | Your computation of the fractional derivative of $y^{-3}$ is strange. Differentiating $2x-1$ times should give (a multiple of) $y$ to the $-3-(2x-1)=-2x-2$, and not $-(4+x)$. You can check the Wikipedia section. For questions 2 and 3, I don't know. | |
| Feb 6, 2022 at 14:58 | history | edited | Max Lonysa Muller |
added a tag
|
|
| Feb 6, 2022 at 14:57 | comment | added | Max Lonysa Muller | @FrançoisBrunault Right, that is good to know. I wonder by the way if you have ideas on questions (1) through (3) ? | |
| Feb 6, 2022 at 14:47 | comment | added | François Brunault | It will depend on how $p,n$ go to infinity. One should look at the general term of the series, namely $B_{2p}/(2p)! \cdot f^{(2p-1)}(n)$. It is easy to estimate in your case, and $n$ must be at least $cp$ for some $c>0$ (I haven't done the precise computation), in order for the series to converge. | |
| Feb 6, 2022 at 11:20 | comment | added | Max Lonysa Muller | @FrançoisBrunault fair enough. But in the example I chose with $f(x) = 1/x^{3}$, $R_{p}$ does converge to zero when $p, n \to \infty$, right? | |
| Feb 5, 2022 at 12:37 | comment | added | François Brunault | If you fix $m$ and $n$ then the error term $R_p$ most often won't converge to 0. One should choose $n$ depending on $p$. | |
| Feb 5, 2022 at 11:18 | history | edited | Max Lonysa Muller | CC BY-SA 4.0 |
improved formatting
|
| Feb 5, 2022 at 11:11 | history | asked | Max Lonysa Muller | CC BY-SA 4.0 |