Timeline for Formula for volume of $n$-ball for negative $n$
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 20, 2020 at 6:35 | comment | added | Anixx | I already asked this question here: math.stackexchange.com/questions/1176034/… There are some answers. | |
| Apr 19, 2020 at 18:04 | answer | added | Anixx | timeline score: 0 | |
| Apr 18, 2020 at 3:32 | answer | added | Anixx | timeline score: 5 | |
| Apr 6, 2020 at 7:35 | review | Close votes | |||
| Apr 6, 2020 at 22:23 | |||||
| Apr 6, 2020 at 0:02 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Mar 7, 2020 at 10:01 | comment | added | Oscar Cunningham | According to wikipedia, $\Gamma(\frac{1}{2}-m) = \frac{(-4)^mm!}{(2m)!}\sqrt{\pi}$. Substituting this in to the above formula gives $|B^{-(2m+1)}| = \frac{(2m)!}{(-\frac{\pi}{4})^mm!}$. | |
| Mar 7, 2020 at 2:43 | comment | added | Sam Hopkins | Maybe en.wikipedia.org/wiki/Reflection_formula is relevant here? | |
| Mar 6, 2020 at 22:54 | history | edited | YCor | CC BY-SA 4.0 |
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| Mar 6, 2020 at 20:46 | comment | added | Bazin | Here is a funny formula: with $\nu !=\Gamma (\nu+1)$, we have $$ \sum_{\nu\in \mathbb N\cup (\mathbb N+\frac12)}\frac{π^\nu}{\nu !} R^{2\nu}=e^{π R^2} +\sum_{k\in \mathbb N}\frac{π^{k+\frac12}}{(k+\frac12)!} R^{2k+1} =\sum_{\nu\in \mathbb N\cup (\mathbb N+\frac12)}\vert \mathbb B^{2\nu}\vert R^{2\nu} =\sum_{n\in \mathbb N} \vert \mathbb B^{n}\vert R^{n}. $$ | |
| Mar 6, 2020 at 10:12 | comment | added | gmvh | It can occur in the dimensional regularization of Feynman diagram integrals in quantum field theory, but I don't think it has too much significance there. | |
| Mar 4, 2020 at 15:28 | comment | added | James Propp | Pure curiosity. | |
| Mar 4, 2020 at 14:22 | comment | added | Piotr Hajlasz | You should explain the context why you are asking this question to make it more relevant. | |
| Mar 4, 2020 at 2:50 | review | Close votes | |||
| Mar 4, 2020 at 16:43 | |||||
| Mar 4, 2020 at 1:12 | history | asked | James Propp | CC BY-SA 4.0 |