Timeline for Calculation of Riesz energy for balls
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Aug 14, 2023 at 6:16 | vote | accept | Sarthak | ||
| Aug 3, 2023 at 22:26 | comment | added | fedja | @MateuszKwaśnicki Only at integers and half-integers. Otherwise it is a 1-D integral that is useful and reasonably fast convergent at $\infty$, but the singularity at $0$ is still on the way of efficient numeric evaluation of it. But I'll grant you that for odd $d$ you have it since only the ratio of two values with integer difference matters there in your final formula. I didn't expect that much, so you've got me here. :-) | |
| Aug 3, 2023 at 21:44 | comment | added | Mateusz Kwaśnicki | @fedja: Does $\Gamma(\ldots)$ count as a neat formula in terms of $\pi$ and $e$? :-) | |
| Aug 3, 2023 at 21:42 | answer | added | Mateusz Kwaśnicki | timeline score: 4 | |
| Aug 3, 2023 at 12:22 | answer | added | Iosif Pinelis | timeline score: 3 | |
| Aug 3, 2023 at 9:53 | comment | added | Sarthak | I am not asking about neat formula. I am saying even if the constant is C how to evaluate the integral as it's not essentially $|x|^{-s}$. I mean say $U=B(x_0,r)$ then what is the power of $r$ it's coming when I am doing the integration. It's not over one ball it's over same ball which I am bit confused. | |
| Aug 3, 2023 at 2:18 | comment | added | fedja | I doubt very much that there is a neat formula in terms of $\pi$ and $e$ of the coefficient in front of the appropriate power of the ball radius, but a natural question to ask is "why do you want to evaluate it at all? Aren't all positive constants essentially the same?". | |
| S Aug 2, 2023 at 18:25 | review | First questions | |||
| Aug 2, 2023 at 18:51 | |||||
| S Aug 2, 2023 at 18:25 | history | asked | Sarthak | CC BY-SA 4.0 |