Question

Non-trivial problems solvable in $\mathscr{O}(1)$?

score 106 · Answer 1 · 2026-03-30 13:06:52

106

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Non-trivial problems solvable in $\mathscr{O}(1)$?

Published on 30 Mar 2026 - 13:06

score 31 · Answer 2 · 2026-03-26 17:30:11

31

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How to find normalizing constants $c_n,d_n$ for weak convergence?

Published on 26 Mar 2026 - 17:30

score 62 · Answer 3 · 2020-01-12 17:34:31

62

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How do I prove that $3n\log(n!) \in O(n^2\log n)$?

Published on 12 Jan 2020 - 17:34

score 47 · Answer 4 · 2020-01-12 17:57:29

Prove that if $\lim_{x\to 0} \frac{f(x)}{x} = 1$, then the sequence $a_n = \left(\sum_{k=1}^n f\!\left(\frac{1}{k}\right)\right) - \ln n$ converges

score 142 · Answer 5 · 2026-04-01 06:29:04

142

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Question about the sequence of moments of a continuous function

Published on 01 Apr 2026 - 6:29

score 77 · Answer 6 · 2026-03-25 23:13:10

77

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Develop asymptotic as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \sum_{i=1}^{k} \sum_{d \mid i (2k-i), d > N} 1$

Published on 25 Mar 2026 - 23:13

score 513 · Answer 7 · 2026-04-03 20:06:11

513

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Showing that $p_n = n\log n + n\log \log n + O(n)$ (simplified prime approximation)

Published on 03 Apr 2026 - 20:06

score 53 · Answer 8 · 2026-04-02 13:35:34

53

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Asymptotic behavior of $n$-fold iterate near the origin

Published on 02 Apr 2026 - 13:35

score 97 · Answer 9 · 2026-04-08 02:27:24

97

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Asymptotic expression for discrete random walk

Published on 08 Apr 2026 - 2:27

score 159 · Answer 10 · 2026-03-26 19:01:56

159

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If an asymptotic expansion is valid as $\text{Re}(z)\to\infty$, must it be valid as $\text{Im}(z)\to\infty$?

Published on 26 Mar 2026 - 19:01

score 39 · Answer 11 · 2020-01-19 04:10:58

39

Views

How to prove f(n) is either O or Ω or Θ of g(n)?

Published on 19 Jan 2020 - 4:10

score 62 · Answer 12 · 2026-03-29 18:13:34

62

Views

Big-theta: are (n-2)! and n! in different growth orders/efficiency classes?

Published on 29 Mar 2026 - 18:13

score 58 · Answer 13 · 2020-01-19 20:23:29

58

Views

Convergence in probability implies equality with probability approaching 1?

Published on 19 Jan 2020 - 20:23

score 57 · Answer 14 · 2020-01-20 12:17:31

57

Views

Big $O$: True or false statements

Published on 20 Jan 2020 - 12:17

score 174 · Answer 15 · 2026-04-01 09:55:34

174

Views

Asymptotic Analysis of $f(n)=nf(n-1)+(n-1)f(n-2)$

Published on 01 Apr 2026 - 9:55

List Question

Non-trivial problems solvable in $\mathscr{O}(1)$?

How to find normalizing constants $c_n,d_n$ for weak convergence?

How do I prove that $3n\log(n!) \in O(n^2\log n)$?

Prove that if $\lim_{x\to 0} \frac{f(x)}{x} = 1$, then the sequence $a_n = \left(\sum_{k=1}^n f\!\left(\frac{1}{k}\right)\right) - \ln n$ converges

Question about the sequence of moments of a continuous function

Develop asymptotic as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \sum_{i=1}^{k} \sum_{d \mid i (2k-i), d > N} 1$

Showing that $p_n = n\log n + n\log \log n + O(n)$ (simplified prime approximation)

Asymptotic behavior of $n$-fold iterate near the origin

Asymptotic expression for discrete random walk

If an asymptotic expansion is valid as $\text{Re}(z)\to\infty$, must it be valid as $\text{Im}(z)\to\infty$?

How to prove f(n) is either O or Ω or Θ of g(n)?

Big-theta: are (n-2)! and n! in different growth orders/efficiency classes?

Convergence in probability implies equality with probability approaching 1?

Big $O$: True or false statements

Asymptotic Analysis of $f(n)=nf(n-1)+(n-1)f(n-2)$

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