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Asymptotic behavior of functions, asymptotic series and related topics

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 …
Gerhard Paseman's user avatar
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 …
Gerhard Paseman's user avatar