Timeline for What function is a Gaussian integral
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 5, 2015 at 3:04 | vote | accept | jian | ||
| Oct 3, 2015 at 11:13 | comment | added | shasta | Comment on the above comment. See now that I completely misunderstood the question being asked. | |
| Oct 3, 2015 at 6:15 | comment | added | shasta | A simple and natural characterisation was already used by Clark Maxwell to deduce what is now known as the Maxwell-Boltzmann formula for the distribution of molecular velocities in a gas. Its density is the only function of two variables which depends only on the distance from the origin and is representable as a product of two functions of one varable. (we give the two-dimensional version for simplicity). Maxwell solved the corresponding functional equation by inspection but it is easy to give a rigorous proof that the only solution (up to constants) is the Gaussian kernel $\exp (x^2+y^2)$. | |
| Oct 3, 2015 at 4:03 | answer | added | Hicham | timeline score: 4 | |
| Oct 3, 2015 at 3:44 | comment | added | user1504 | There is no inverse function. If $f$ is antisymmetric around $\mu$, then $g(\mu,\delta) = 0$. There are many such functions (e.g. $f(x) = (x-\mu)^{2n+1}$). | |
| Oct 3, 2015 at 1:40 | history | asked | jian | CC BY-SA 3.0 |