Question

$a_{n+1}=\ln (1+ \arctan(a_n))$, convergence of sequence, asymptotic approximation with $cn^\alpha$, and convergence of $\sum_{n=1}^{+\infty}a_nx^n$

score 95 · Answer 1 · 2020-04-23 15:23:02

95

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$a_{n+1}=\ln (1+ \arctan(a_n))$, convergence of sequence, asymptotic approximation with $cn^\alpha$, and convergence of $\sum_{n=1}^{+\infty}a_nx^n$

Published on 23 Apr 2020 - 15:23

score 51 · Answer 2 · 2026-04-11 14:32:49

51

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Questions about induction and Big O

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score 883 · Answer 3 · 2026-04-11 12:18:46

883

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Understanding little $o$ and big $O$ notation

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score 33 · Answer 4 · 2020-04-24 06:28:11

33

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Property of 'little oh' notation from Tom Apostol Vol.1

Published on 24 Apr 2020 - 6:28

score 41 · Answer 5 · 2026-04-11 13:53:46

41

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How many associative functions are there?

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score 36 · Answer 6 · 2026-04-03 01:04:10

36

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Big O notation on polynomials

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score 41 · Answer 7 · 2026-04-03 00:59:02

41

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log(n)^k = O(n^epsilon)

Published on 03 Apr 2026 - 0:59

score 92 · Answer 8 · 2020-04-24 20:15:30

92

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Estimating $\sum_{n=1}^N \cos(t\log n)$

Published on 24 Apr 2020 - 20:15

score 75 · Answer 9 · 2026-04-09 15:14:31

75

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Derivative of Little o

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score 119 · Answer 10 · 2026-03-25 15:53:37

119

Views

On the asymptotics of $\sum_{k=1}^{n^2} \{\sqrt{k}\} $

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score 119 · Answer 11 · 2026-04-01 19:15:36

119

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How can I prove $\lim_{s\to 1^-}\sum_{n=0}^{\infty}\left(-1\right)^n\frac{\Gamma(1+ns)}{\Gamma(1+n)}=\frac{1}{2}$

Published on 01 Apr 2026 - 19:15

score 77 · Answer 12 · 2020-04-26 11:15:18

77

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Series expression by using Puiseux series

Published on 26 Apr 2020 - 11:15

score 73 · Answer 13 · 2020-04-26 19:43:49

73

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What are the “mild conditions” Wikipedia describes that allow asymptotic equivalence?

Published on 26 Apr 2020 - 19:43

score 155 · Answer 14 · 2020-04-26 21:58:56

155

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Is $n\log n = \Omega (n^{log_4(3) + \varepsilon})$?

Published on 26 Apr 2020 - 21:58

score 72 · Answer 15 · 2026-03-26 04:34:17

72

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Commuting fraction of $F_n$

Published on 26 Mar 2026 - 4:34

List Question

$a_{n+1}=\ln (1+ \arctan(a_n))$, convergence of sequence, asymptotic approximation with $cn^\alpha$, and convergence of $\sum_{n=1}^{+\infty}a_nx^n$

Questions about induction and Big O

Understanding little $o$ and big $O$ notation

Property of 'little oh' notation from Tom Apostol Vol.1

How many associative functions are there?

Big O notation on polynomials

log(n)^k = O(n^epsilon)

Estimating $\sum_{n=1}^N \cos(t\log n)$

Derivative of Little o

On the asymptotics of $\sum_{k=1}^{n^2} \{\sqrt{k}\} $

How can I prove $\lim_{s\to 1^-}\sum_{n=0}^{\infty}\left(-1\right)^n\frac{\Gamma(1+ns)}{\Gamma(1+n)}=\frac{1}{2}$

Series expression by using Puiseux series

What are the “mild conditions” Wikipedia describes that allow asymptotic equivalence?

Is $n\log n = \Omega (n^{log_4(3) + \varepsilon})$?

Commuting fraction of $F_n$

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