Timeline for Asymptotics of the general second order affine recursion
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 7, 2019 at 1:13 | vote | accept | Hans | ||
| Nov 7, 2019 at 1:10 | vote | accept | Hans | ||
| Nov 7, 2019 at 1:13 | |||||
| Oct 12, 2019 at 19:19 | comment | added | Hans | @FedorPetrov: Do you have any ideas or suggestions? | |
| Oct 12, 2019 at 19:14 | comment | added | Hans | How did you obtain your ansatz, from numerical computation and plotting the graph? | |
| Oct 11, 2019 at 23:04 | answer | added | Beans | timeline score: 3 | |
| Oct 11, 2019 at 19:26 | comment | added | Henri Cohen | @Hans: I said I believe because I have no rigorous proof, it depends on the initial values. I simply use the Ansatz that the asymptotic is of the form I give (with an extra subexponential term $\exp(-u\sqrt{n})$ which is not needed here), and find the constants. In this way you can also obtain an asymptotic expansion in $1/n$. The only unknown is the constant $C$ which depends on the initial values. | |
| Oct 11, 2019 at 16:31 | comment | added | Hans | @Bullet51: I have tried that and gotten a second-order linear nonhomogeneous ODE which I cannot solve directly (without using the Frobenius method). | |
| Oct 11, 2019 at 16:29 | comment | added | Hans | @HenriCohen: Could you please write out the details of the derivation as an answer? | |
| Oct 11, 2019 at 9:35 | comment | added | LeechLattice | What about trying exponential generating functions? | |
| Oct 11, 2019 at 8:36 | comment | added | Henri Cohen | $C.n!\alpha_1^nn^{\alpha_2/\alpha_1+\alpha_3/\alpha_1^2}$ I believe if $\alpha_1\alpha_3\ne0$ (similar formulas otherwise). | |
| Oct 11, 2019 at 7:46 | comment | added | Hans | @FedorPetrov: Just clarified that in the question. | |
| Oct 11, 2019 at 7:46 | history | edited | Hans | CC BY-SA 4.0 |
added 12 characters in body
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| Oct 11, 2019 at 7:30 | comment | added | Fedor Petrov | is $\delta\in \{0,1\}$ fixed or may depend on $n$? | |
| Oct 11, 2019 at 7:04 | history | edited | Hans | CC BY-SA 4.0 |
added 177 characters in body
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| Oct 11, 2019 at 6:57 | comment | added | Hans | @IlyaBogdanov: Yes, I did indeed. I added the link to my frustrated attempt at an example. | |
| Oct 11, 2019 at 6:56 | history | edited | Hans | CC BY-SA 4.0 |
Added an example.
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| Oct 11, 2019 at 6:02 | comment | added | Ilya Bogdanov | Did you try generating functions? | |
| Oct 11, 2019 at 0:42 | history | asked | Hans | CC BY-SA 4.0 |