Timeline for Integral of product of Hermite polynomials w.r.t marginal distribution of first two-coordinate of random vector on unit-sphere
Current License: CC BY-SA 4.0
10 events
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| Oct 11, 2021 at 14:47 | comment | added | dohmatob | Ah, yes that makes sense on second thought. Thanks. Any idea what the coefficient of $t^k$ (for $k \ge 2$; especially the case $k=2$) would be ? I'm suspecting it would be something like $\mathcal O(1/d^k)$. To get this kind of information, one would have to use a higher-order expansion of the Hermite polynomial expressions (in the integral) around $r=0$, right ? | |
| Oct 11, 2021 at 14:42 | comment | added | Carlo Beenakker | no, I would think that the error term is of order $1/d^2$. | |
| Oct 11, 2021 at 14:31 | comment | added | dohmatob | Do we have a rough idea how small the error term ignored in the above approximation of $s_{nm}$ is ? For example, is it by any chance of order $\mathcal O(1/d^{2 + \varepsilon})$ for some $\varepsilon>0$ ? | |
| Oct 10, 2021 at 18:19 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Oct 10, 2021 at 18:16 | vote | accept | dohmatob | ||
| Oct 10, 2021 at 18:16 | comment | added | dohmatob | This is quite instructive. Thanks! | |
| Oct 10, 2021 at 18:13 | vote | accept | dohmatob | ||
| Oct 10, 2021 at 18:13 | |||||
| Oct 10, 2021 at 17:55 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Oct 10, 2021 at 17:48 | history | edited | Carlo Beenakker | CC BY-SA 4.0 |
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| Oct 10, 2021 at 17:26 | history | answered | Carlo Beenakker | CC BY-SA 4.0 |