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Results tagged with asymptotics
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user 3206
Asymptotic behavior of functions, asymptotic series and related topics
1
vote
Asymptotic growth of recurrence relation $x_n=\min\limits_{n_1+n_2=n}(a(x_{n_1}+x_{n_2})+2n_...
Some back-of-the-frontal-lobe calculations:
One gets $x_2=2$ and $x_3=2a+4$, given the limited number of sums. For $x_4$, we have a choice of
$4a+8$ or $2a^2 +4a +6$, and for $x_5$ either $2a^2 +6a …
- 3,209
2
votes
Asymptotic behaviour of sequence
For sums like this, usually one term dominates. Taking $p(n)=n^d$ to play with, consider
when $\binom{(n-k)^d}{k} \lt \binom{(n-k-1)^d}{k+1}$ stops holding. This is not far from
when $(k+1) \lt (\fr …
- 3,209