Timeline for Simple/efficient representation of Stirling numbers of the first kind
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
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| Aug 3, 2023 at 15:41 | comment | added | Tom Copeland | Rather linked post. Note the equations give a polynomial in y of degree n-k. | |
| Aug 2, 2023 at 20:58 | comment | added | Tom Copeland | @TymaGaidash, the last equality is the limit when evaluated at y =0. It's been several years since I've looked at it, but if you have specific questions about the linked paper from which these results issue, feel free to ask. Use the online app DESMOS to graph the first two sums with y changed to x and, say, n=3 to spot check the equations. | |
| Aug 2, 2023 at 18:04 | comment | added | Тyma Gaidash | @TomCopeland That is why it is being asking if you knew a way to evaluate the limit. | |
| Aug 2, 2023 at 18:04 | comment | added | Tom Copeland | @TymaGaidash, can you give me an example of how you would obtain a number other than $S_1(n,k)$ in the limit? | |
| Aug 2, 2023 at 12:05 | comment | added | Тyma Gaidash | How would you evaluate the limit to get a single series? | |
| Sep 5, 2015 at 1:22 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Added identity
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| Sep 4, 2015 at 21:25 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Exchanged factors to avoid potential confusion on summation
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| Sep 4, 2015 at 17:56 | comment | added | Gottfried Helms | Ahh, thanks, that looks very promising. | |
| Sep 4, 2015 at 17:34 | comment | added | Tom Copeland | @Gottfried, I included a link to a simple derivation of the formula, including an equivalent matrix formula. | |
| Sep 4, 2015 at 17:31 | history | edited | Tom Copeland | CC BY-SA 3.0 |
Link to derivation in response to comment
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| Sep 4, 2015 at 10:47 | comment | added | Gottfried Helms | This looks to me like using an asymptotical inverse of the infinite Vandermondematrix $V_{r,c}=r^c$ (which of course does not exist). Like $V= S_2 \cdot \ ^dF \cdot P$ then $V \cdot P^{-1} \cdot \ ^dF^{-1} \cdot V = S_2 $ and then the inversion: $V^{-1} \cdot \ ^dF \cdot P =S_1 $ where of course we cannot exactly use $V$ because the inversion would produce singularities. Did you get your formula by something like this? ($P$: upper triangular binomialmatrix, $S_2$ Stirling numbers 2nd kind, $ \ ^dF$ diagonalmatrix of factorials) | |
| Sep 4, 2015 at 6:54 | history | answered | Tom Copeland | CC BY-SA 3.0 |