Timeline for Closed form of a nonlinear recurrence sequence.
Current License: CC BY-SA 2.5
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 4, 2010 at 5:46 | comment | added | Douglas S. Stones | Do you actually mean they never have closed forms (i.e. can it be proved that a "closed form" (defined in some concrete manner) doesn't exist in some cases?), or that we're currently unable to find them (i.e. it is possible that someone in the future could find one)? | |
| Jan 21, 2010 at 14:33 | comment | added | Kevin Buzzard | [Or x_{n+1}=cx_n^2, he said, pedantically] | |
| Jan 21, 2010 at 14:02 | answer | added | Julián Aguirre | timeline score: 1 | |
| Jan 21, 2010 at 4:00 | comment | added | Qiaochu Yuan | In fact, to my knowledge the only quadratic recurrence which has anything like a closed form is (anything that reduces to) x_{n+1} = 2x_n^2 - 1 because of the cosine double-angle formula. | |
| Jan 21, 2010 at 3:55 | comment | added | Gjergji Zaimi | mathoverflow.net/questions/9660/… | |
| Jan 21, 2010 at 3:50 | comment | added | Jason Knight | Seems like I'm out of luck. I just compared the function in question with logistic maps (the similarity is striking). No wonder I was butting my head against a wall. | |
| Jan 21, 2010 at 3:39 | comment | added | Zev Chonoles | Qiaochu is right. Whatever general results there are for nonlinear recurrences, they should be in here: books.google.com/… I own this book myself, but have only studied the parts of it relevant to linear recurrences, so I can't direct you to anything specific. | |
| Jan 21, 2010 at 3:29 | comment | added | Jason Knight | I changed the title as suggested. | |
| Jan 21, 2010 at 3:28 | comment | added | Qiaochu Yuan | Generally speaking, nonlinear recurrences almost never have closed forms. | |
| Jan 21, 2010 at 3:28 | history | edited | Jason Knight | CC BY-SA 2.5 |
edited title; edited title
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| Jan 21, 2010 at 3:08 | comment | added | Zev Chonoles | I think you may want to retitle this something like "Closed form for a nonlinear recurrence sequence?" | |
| Jan 21, 2010 at 2:26 | history | asked | Jason Knight | CC BY-SA 2.5 |