Timeline for Sum of Gaussian pdfs
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 30, 2017 at 19:47 | comment | added | eigenjohnson | B-splines are a partition of unity, and the limit as the order goes to infinity of a B-spline is a Gaussian. | |
| Oct 27, 2017 at 9:58 | comment | added | Hans Lundmark | This phenomenon is the basis for "approximate approximations", a semi-analytical numerical method for solving differential equations, developed by V. Mazya and G. Schmidt. See Section 1.1.1 in their book: amazon.com/… | |
| Oct 27, 2017 at 2:18 | comment | added | Mark Schultz-Wu | I'm just a novice in the field, but I believe this is closely related to the smoothing parameter of a lattice in lattice-based cryptography. | |
| Oct 26, 2017 at 17:30 | answer | added | Dustin G. Mixon | timeline score: 9 | |
| Oct 26, 2017 at 15:59 | answer | added | Steve Huntsman | timeline score: 6 | |
| Oct 26, 2017 at 15:51 | vote | accept | Anthony Quas | ||
| Oct 26, 2017 at 11:50 | comment | added | Carl Witthoft | "The mass of the Earth is almost exactly $\pi$ milliJupiters" (what-if.xkcd.com) . Sometimes things just are coincidental. But this question does remind me of the Partition of Unity en.wikipedia.org/wiki/Partition_of_unity | |
| Oct 26, 2017 at 7:09 | answer | added | Nemo | timeline score: 36 | |
| Oct 26, 2017 at 6:51 | comment | added | Anthony Quas | I'm pretty sure it's not exact. If you compute $F(0)-F(\frac 12)$, the result (using only $n$'s in the range $-10$ to 10) is $1.07012\times10^{-8}$. The error from truncating at the 10th term is something like $e^{-50}$, which is much smaller than this. | |
| Oct 26, 2017 at 6:50 | comment | added | Dirk | A equivalent question to ask is: Why does $\sum_{n\in\mathbf{Z}} e^{-xn-n^2/2}$ is almost (or exactly) equal to $e^{x^2/2}\sqrt{2\pi}$? | |
| Oct 26, 2017 at 6:48 | comment | added | Dirk | Are you sure that it is only remarkably close or may it be exact? (My crude numerical experiment gave exactly one, but then, it may be too crude…). | |
| Oct 26, 2017 at 6:30 | history | asked | Anthony Quas | CC BY-SA 3.0 |