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Results tagged with closed-form-expressions
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user 11926
For questions that specifically ask for determining a closed form of equations, integrals etc.
15
votes
Find a formula for the recurrent sequence $q_{n+1}=q_n(q_n+1)+1$
I'm not quite sure what you mean by an "analytic formula." As Fedor Petrov indicated, there is unlikely to be a closed formula. However, there is a convergent power series. More precisely, consider it …
- 47.4k
14
votes
Find a formula for the recurrent sequence $q_{n+1}=q_n(q_n+1)+1$
This is a second answer with a somewhat different viewpoint from my other answer. It is an expansion, in some sense, of Gerry Myerson's answer. There is a general theory for estimating these sorts of …
- 47.4k
4
votes
About $a_n = \frac{a_{n-1}(a_{n-1} + C)}{a_{n-2}}.$
Sometimes it's helpful to look at problems of this sort in a slightly more general geometric framework, especially if you want to work over other fields. You can model your problem as a map of $\mathb …
- 47.4k