Timeline for Polynomial related to lognormal moments
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| Mar 28, 2017 at 21:59 | comment | added | Max Alekseyev | In fact, $\sum_{k=0}^r (-1)^{r-k}\binom{r}{k}k^n = r!\cdot S(n,r)$, where $S(,)$ are Stirling numbers of second kind, and they are zero if $n<r$. | |
| Mar 28, 2017 at 10:00 | vote | accept | David Wright | ||
| Mar 28, 2017 at 9:14 | comment | added | Fedor Petrov | You may write $q(x)=p(x)\cdot (1-x)^{-m}$, $m=\lceil r/2\rceil$, and look at this as a power series. This gives some formulae for coefficients of $q$. I do not know whether this is ok for you. | |
| Mar 28, 2017 at 9:09 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
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| Mar 28, 2017 at 8:31 | comment | added | David Wright | Brilliant! Took me 15 minutes to comprehend each bit, but this is a fine proof.I messed around a bit more to see if there s some way I could construct $q(x)$ from the derivatives of $p(x)$, but that doesn't seem to be working out for me. Polynomial division isn't really a good approach, numerically. I don't suppose you see a way to construct $q(x)$ from this result? Thanks, in any case. | |
| Mar 28, 2017 at 6:42 | history | answered | Fedor Petrov | CC BY-SA 3.0 |