Timeline for Two-term recurrence relation
Current License: CC BY-SA 4.0
17 events
| when toggle format | what | by | license | comment | |
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| S Feb 13, 2021 at 3:01 | history | bounty ended | CommunityBot | ||
| S Feb 13, 2021 at 3:01 | history | notice removed | CommunityBot | ||
| Feb 5, 2021 at 18:31 | comment | added | Max Alekseyev | @BrendanMcKay: In the context of the corresponding ODEs (cf. my answer), this would be equivalent to transforming the system of two first-order ODEs to a single second-order ODE by substitution as pointed out by Alexey. | |
| S Feb 5, 2021 at 1:26 | history | bounty started | Kung Yao | ||
| S Feb 5, 2021 at 1:26 | history | notice added | Kung Yao | Authoritative reference needed | |
| Feb 4, 2021 at 2:23 | comment | added | Brendan McKay | The first equation can be solved for $b_n$, then that value can be substituted into the second equation. This gives a recurrence involving only $\{a_n\}$ with coefficients rational in $n$. I assume there is a theory about such recurrences. | |
| Feb 3, 2021 at 19:55 | comment | added | Iosif Pinelis | @KungYao : I think it could be helpful for some MO users to see the details of what you mentioned in your latter comment. | |
| Feb 3, 2021 at 17:28 | answer | added | Max Alekseyev | timeline score: 2 | |
| Feb 3, 2021 at 17:24 | comment | added | Kung Yao | @IosifPinelis I do, this comes from the matching conditions of coefficients in an ODE and numerically that ODE has a solution (for certain choices of $\lambda$ at least.) In particular, when $\lambda$ is the third root of unity. | |
| Feb 3, 2021 at 17:19 | comment | added | Iosif Pinelis | Do you have reasons to believe that such initial conditions exist? | |
| Feb 3, 2021 at 17:11 | comment | added | Kung Yao | @AntoineLabelle thanks, is implemented now. | |
| Feb 3, 2021 at 17:11 | history | edited | Kung Yao | CC BY-SA 4.0 |
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| Feb 3, 2021 at 2:44 | history | edited | Kung Yao | CC BY-SA 4.0 |
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| Feb 3, 2021 at 2:10 | comment | added | Antoine Labelle | As $|\lambda|=1$ doesn't $\lambda^*=\lambda^{-1}$? | |
| Feb 3, 2021 at 0:13 | history | edited | Kung Yao | CC BY-SA 4.0 |
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| Feb 2, 2021 at 23:51 | history | edited | Kung Yao | CC BY-SA 4.0 |
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| Feb 2, 2021 at 23:45 | history | asked | Kung Yao | CC BY-SA 4.0 |