Question

Complex Analysis Extension of Bernoulli Number Generating function

score 389 · Answer 1 · 2026-03-25 17:28:16

389

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Complex Analysis Extension of Bernoulli Number Generating function

Published on 25 Mar 2026 - 17:28

score 213 · Answer 2 · 2019-01-27 15:28:48

213

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Infimum of sum of two values.

Published on 27 Jan 2019 - 15:28

score 270 · Answer 3 · 2026-03-22 20:31:03

270

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Are these limits correct? $\lim_{n\to \infty}\text{sup} \frac{\lambda (n)}{n}=1$ and $\lim_{n\to \infty}\text{inf} \frac{\lambda (n)}{n}=0$ exist?

Published on 22 Mar 2026 - 20:31

score 95 · Answer 4 · 2019-01-27 22:11:36

95

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If $\lim \text{sup}_{n\to\infty}X_n≠\lim \text{inf}_{n\to\infty}X_n$, can we say "limit doesn't exist"?

Published on 27 Jan 2019 - 22:11

score 45 · Answer 5 · 2019-01-30 09:38:11

45

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$\limsup_{n\to\infty}{a_n}^{b_n}= \limsup_{n\to\infty}{a_n}^{\lim\limits_{n\to\infty}b_n}$ under certian conditions.

Published on 30 Jan 2019 - 9:38

score 52 · Answer 6 · 2019-02-04 00:23:51

52

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Show that the distance $d(x)$ of a point $x = (x_k)\in \ell_\infty$ to $c_0$ is equal to $\limsup_{k\to\infty} |x_k|.$

Published on 04 Feb 2019 - 0:23

score 30 · Answer 7 · 2019-02-05 14:35:48

30

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Calculation of $\liminf_{n\to\infty} \frac{1}{1+e^{nx}}e^{-x^2/n} $ on $\mathbb{R}^-$

Published on 05 Feb 2019 - 14:35

score 77 · Answer 8 · 2026-02-23 06:27:17

77

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Silly question on lower semi-continuity

Published on 23 Feb 2026 - 6:27

score 1.3k · Answer 9 · 2019-02-06 12:08:48

1.3k

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Radius of convergence of power series $\sum_{n=0}^{\infty} n!x^{n^2}$

Published on 06 Feb 2019 - 12:08

score 318 · Answer 10 · 2019-02-10 06:33:32

318

Views

Limit inferior of product of two non negative bounded sequences

Published on 10 Feb 2019 - 6:33

score 109 · Answer 11 · 2026-03-25 19:07:22

109

Views

$\limsup_{n \to \infty}\{\frac{X_{n}}{\log{(n)}}\leq\epsilon\}\subseteq \{\liminf_{n \to \infty}\frac{X_{n}}{\log{(n)}}\leq\epsilon\}$

Published on 25 Mar 2026 - 19:07

score 1k · Answer 12 · 2019-02-15 15:21:04

1k

Views

Stuck at proving whether the sequence is convergent or not

Published on 15 Feb 2019 - 15:21

score 779 · Answer 13 · 2019-02-17 15:35:44

779

Views

(Proof verification) Showing that the two $\limsup$ definitions are equivalent

Published on 17 Feb 2019 - 15:35

score 94 · Answer 14 · 2019-02-20 03:13:18

94

Views

A property of limit supremum

Published on 20 Feb 2019 - 3:13

score 311 · Answer 15 · 2019-02-20 08:01:20

311

Views

Let $(a_n),(b_n) $ be sequences of positive real numbers such that $na_n<b_n<n^2a_n$

Published on 20 Feb 2019 - 8:01

List Question

Complex Analysis Extension of Bernoulli Number Generating function

Infimum of sum of two values.

Are these limits correct? $\lim_{n\to \infty}\text{sup} \frac{\lambda (n)}{n}=1$ and $\lim_{n\to \infty}\text{inf} \frac{\lambda (n)}{n}=0$ exist?

If $\lim \text{sup}_{n\to\infty}X_n≠\lim \text{inf}_{n\to\infty}X_n$, can we say "limit doesn't exist"?

$\limsup_{n\to\infty}{a_n}^{b_n}= \limsup_{n\to\infty}{a_n}^{\lim\limits_{n\to\infty}b_n}$ under certian conditions.

Show that the distance $d(x)$ of a point $x = (x_k)\in \ell_\infty$ to $c_0$ is equal to $\limsup_{k\to\infty} |x_k|.$

Calculation of $\liminf_{n\to\infty} \frac{1}{1+e^{nx}}e^{-x^2/n} $ on $\mathbb{R}^-$

Silly question on lower semi-continuity

Radius of convergence of power series $\sum_{n=0}^{\infty} n!x^{n^2}$

Limit inferior of product of two non negative bounded sequences

$\limsup_{n \to \infty}\{\frac{X_{n}}{\log{(n)}}\leq\epsilon\}\subseteq \{\liminf_{n \to \infty}\frac{X_{n}}{\log{(n)}}\leq\epsilon\}$

Stuck at proving whether the sequence is convergent or not

(Proof verification) Showing that the two $\limsup$ definitions are equivalent

A property of limit supremum

Let $(a_n),(b_n) $ be sequences of positive real numbers such that $na_n<b_n<n^2a_n$

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