Timeline for Derive a closed-form expression of this recursive formula
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 12, 2023 at 16:57 | comment | added | Thomas Kojar | I guess. You can try that approach with the power series and see. They just shift indices around and then Taylor expand. | |
| Mar 12, 2023 at 11:17 | comment | added | K. Bountrogiannis | @ThomasKojar If we assume that $S_{0,k}$ is just a variable, could you at least get an analytic expression involving $S_{0,k}$, $f(r)$ and $g(r)$? | |
| Mar 11, 2023 at 23:17 | comment | added | Thomas Kojar | Just trying it a bit, in order to solve it that way, I needed extra information such as the boundary data $S_{0,k}$ and some relation between $g(r)$ and $g(r+1)$. The boundary data can in principle be determined from the recursion but is tricky. Unless we at least have a known compatible boundary data $S_{0,k}$ , this problem is likely a regular numerical discrete-pde problem with no closed forms. But perhaps there is some other approach or pattern I missed. | |
| Mar 11, 2023 at 22:43 | comment | added | Thomas Kojar | You could try the approach with power series from here math.stackexchange.com/questions/2065067/… | |
| Mar 11, 2023 at 20:49 | comment | added | K. Bountrogiannis | Possibly. But I think they imply that S(r,k) is bounded. | |
| Mar 11, 2023 at 20:46 | comment | added | Martin Rubey | The conditions on $f$ and $g$ seem irrelevant. | |
| Mar 11, 2023 at 20:11 | history | edited | K. Bountrogiannis |
edited tags
|
|
| Mar 11, 2023 at 19:32 | history | asked | K. Bountrogiannis | CC BY-SA 4.0 |