Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with asymptotics
Search options answers only
not deleted
user 498835
Asymptotic behavior of functions, asymptotic series and related topics
8
votes
Accepted
Series with the smallest number whose square is divisible by $n$
I couldn't find a reference, but (as noted in the OEIS page) if we have $k = a b^2$ with squarefree $a$ then $a(k) = ab$, so $$\begin{align*}
\sum_{k\leq x}\frac1{a(k)}
&= \sum_{a b^2 \leq x} \frac{\m …
- 3,319
46
votes
Accepted
A challenging (for me) limit calculation
This limit converges to $\frac{\sqrt3}2$. The idea is that $\sin(x) = x - \frac{x^3}6 + O(x^5)$, so we start with $\frac1{\sqrt n}$ and repeatedly subtract $\frac{x^3}6$. We can approximate this discr …
- 3,319
0
votes
Expected sorting time of random permutation using random comparators
Here's a proof that $\mathbf{E}[X] = O(n^2 \log^2(n))$. Let's assume WLOG $n$ is a power of 2. Let's calculated the expected time until all values bigger than $\frac{n}2$ are in the second half (and a …
- 3,319