Question

Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left\{{\sqrt{{N}^{2}+{k}^{2}}}\right\}$

score 151 · Answer 1 · 2026-03-25 13:58:10

151

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Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left\{{\sqrt{{N}^{2}+{k}^{2}}}\right\}$

Published on 25 Mar 2026 - 13:58

score 528 · Answer 2 · 2026-04-07 21:12:33

528

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If a function is "little oh of something", does it mean that the runtime of that function is strictly less than that?

Published on 07 Apr 2026 - 21:12

score 212 · Answer 3 · 2026-03-26 09:49:20

212

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Asymptotic expansion with repeated roots

Published on 26 Mar 2026 - 9:49

score 176 · Answer 4 · 2026-03-26 12:53:44

176

Views

Convergence of $A_n^{'}A_n$ to $I_k$ in probability implies $A^{-1}_n$ bounded in probability.

Published on 26 Mar 2026 - 12:53

score 39 · Answer 5 · 2020-01-21 19:55:59

39

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$f(n) = O(g(n))$ then $(f(n)+1)=O(g(n))$

Published on 21 Jan 2020 - 19:55

score 107 · Answer 6 · 2026-03-25 23:11:14

107

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Asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} k \sum_{e \mid 2k}\frac{\Lambda \left({e}\right)}{e}$

Published on 25 Mar 2026 - 23:11

score 174 · Answer 7 · 2026-04-07 09:30:24

174

Views

How to solve $f(n) = f(n-1) + f(n-1) f(n-2)$?

Published on 07 Apr 2026 - 9:30

score 582 · Answer 8 · 2026-04-08 02:05:03

582

Views

Primitive and derivative of little $o$

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score 129 · Answer 9 · 2026-03-26 19:19:03

129

Views

Obtaining rates for convergence in probability from rates of convergence in expectation.

Published on 26 Mar 2026 - 19:19

score 103 · Answer 10 · 2020-01-22 16:42:23

103

Views

Big O notation Problems

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score 341 · Answer 11 · 2026-03-25 12:28:22

341

Views

Asymptotic expansion of the Volterra integral equation with series ansatz

Published on 25 Mar 2026 - 12:28

score 215 · Answer 12 · 2026-04-06 16:14:09

215

Views

Finding the leading order contribution to a certain integral.

Published on 06 Apr 2026 - 16:14

score 35 · Answer 13 · 2026-03-26 11:01:38

35

Views

Similar to what polynomials of $1/(1-q)$ does the function $\Gamma (n) (-\log (q))^{-n}$ behave near $q=1$?

Published on 26 Mar 2026 - 11:01

score 44 · Answer 14 · 2020-01-24 06:29:44

44

Views

Asymptote of largest root of polynomial of order $n$

Published on 24 Jan 2020 - 6:29

score 55 · Answer 15 · 2020-01-24 15:55:50

55

Views

Prove a Little o inequality

Published on 24 Jan 2020 - 15:55

List Question

Find the asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} \left\{{\sqrt{{N}^{2}+{k}^{2}}}\right\}$

If a function is "little oh of something", does it mean that the runtime of that function is strictly less than that?

Asymptotic expansion with repeated roots

Convergence of $A_n^{'}A_n$ to $I_k$ in probability implies $A^{-1}_n$ bounded in probability.

$f(n) = O(g(n))$ then $(f(n)+1)=O(g(n))$

Asymptotic expansion as $N \rightarrow \infty$ of $\sum_{k=1}^{\left\lfloor{N/2}\right\rfloor} k \sum_{e \mid 2k}\frac{\Lambda \left({e}\right)}{e}$

How to solve $f(n) = f(n-1) + f(n-1) f(n-2)$?

Primitive and derivative of little $o$

Obtaining rates for convergence in probability from rates of convergence in expectation.

Big O notation Problems

Asymptotic expansion of the Volterra integral equation with series ansatz

Finding the leading order contribution to a certain integral.

Similar to what polynomials of $1/(1-q)$ does the function $\Gamma (n) (-\log (q))^{-n}$ behave near $q=1$?

Asymptote of largest root of polynomial of order $n$

Prove a Little o inequality

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