Timeline for Is there a way to express an power law decay as a series of exponentials?
Current License: CC BY-SA 3.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| 8 hours ago | comment | added | Charlie Parker | I also want to see a full derivation | |
| Jun 19, 2023 at 2:40 | comment | added | Yaroslav Bulatov | @RylanSchaeffer If you restrict $t$ to be $\in [0,1]$, your equation gives $\operatorname{Beta}(r,1)$ distribution | |
| Mar 13, 2021 at 5:26 | comment | added | Rylan Schaeffer | Thank you! I have a small related question: is there some way to interpret $\frac{t^{r-1}}{\Gamma(r)}$ as a probability distribution over $t$? | |
| Feb 26, 2021 at 20:22 | comment | added | Noam D. Elkies | This integral is well known and should be in most integral tables. The change of variable $xt=u$ converts the integral to $x^{-r} \int_0^\infty u^{r-1} e^{-u} \, du$, and $\int_0^\infty u^{r-1} e^{-u} \, du$ is the definition of $\Gamma(r)$. | |
| Feb 26, 2021 at 19:11 | comment | added | Rylan Schaeffer | @NoamD.Elkies could you add a derivation? | |
| Feb 6, 2019 at 21:09 | comment | added | Moustache | @Noam - Could you suggest any textbooks/papers where the formula you quoted is derived? Would be of great help, thanks. | |
| Oct 15, 2016 at 21:25 | comment | added | Will Jagy | Noam, thank you. Between email and a comment of this type, I expected the comment to be less of an intrusion. In future I will use email or forget the thing. Gerry Myerson once made a similar comment when I called his attention to something in this way, so I guess I had this backwards. Sorry. | |
| Oct 15, 2016 at 21:01 | comment | added | Noam D. Elkies | Um, surely this request doesn't belong on this completely unrelated query... (and you have my e-mail address.) To your question, that seems right (though I didn't check the numbers), though probably unnecessary because splitting into several spinor genera requires discriminants of high valuation, and the Leech/Niemeier genus has dicsriminant whose valuations are as smaller as possible! But I've not studied this aspect of the theory carefully enough to be certain of this argument. | |
| Oct 15, 2016 at 15:56 | comment | added | Will Jagy | Dear Noam, could you please take a look at mathoverflow.net/questions/252071/… ? I think my answer is correct, but I also think you would know for sure. | |
| Oct 8, 2016 at 4:50 | history | answered | Noam D. Elkies | CC BY-SA 3.0 |