Timeline for Asymptotic bound for $\sum_{x=0}^\infty \sum_{y=0}^\infty (x+y)^m e^{-\frac{x^2}{2i} - \frac{y^2}{2j}}$ for $i$ and $j$ large
Current License: CC BY-SA 4.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 6, 2021 at 17:22 | comment | added | Iosif Pinelis | @JoshuaErde : This looks good to me. | |
| Jan 6, 2021 at 9:42 | comment | added | Joshua Erde | I'm just discussing with my co-authors the best way to cite this for use in our paper. As I understand it is common to just cite the answers from the website, but I'm not certain about the long term aspects of that, so I would perhaps feel more comfortable (if it would be acceptable to you) citing the answer but also including at least a sketch of the mathematical detail in the paper itself. Does that sound ok, or would you have another suggestion? | |
| Dec 23, 2020 at 20:30 | vote | accept | Joshua Erde | ||
| Dec 18, 2020 at 11:45 | comment | added | Joshua Erde | Both of these answers look brilliant, thank you. It is a shame that this approximation step is so arduous. I will try to find the time to read them closely next week. | |
| Dec 17, 2020 at 4:40 | comment | added | Iosif Pinelis | In the previous answer, it remained to show that the double sum is asymptotic to the corresponding double integral. While the proof of that is straightforward, it is exceedingly nasty. In this alternative proof, we only need to show that an ordinary sum is asymptotic to the ordinary integral. The latter task is also straightforward and also very nasty, but not as nasty as for the double sum. | |
| Dec 17, 2020 at 4:35 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |