Question

Does $f_n(x):=\left(\frac{n^n}{n!}\prod_{k=1}^n\frac{x+\frac{n}{k}}{x^2+\frac{n^2}{k^2}}\right)^{\frac{x}{n}}$ converge uniformly?

score 52 · Answer 1 · 2024-03-25 06:45:21

52

Views

Does $f_n(x):=\left(\frac{n^n}{n!}\prod_{k=1}^n\frac{x+\frac{n}{k}}{x^2+\frac{n^2}{k^2}}\right)^{\frac{x}{n}}$ converge uniformly?

Published on 25 Mar 2024 - 6:45

score 25 · Answer 2 · 2026-02-25 00:13:34

25

Views

Show that the sequence $(f_n)_{n \in \mathbb{N}} \in (C^0([0,2]),||\cdot||_1)$, is a Cauchy-sequence, but does not converge

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score 37 · Answer 3 · 2024-03-31 01:39:29

37

Views

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score 171 · Answer 4 · 2024-03-31 09:17:19

171

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How to rigorously prove that $\sum\limits_{n=1}^ \infty( \frac{1}{4n-1} - \frac{1}{4n} )=\frac{\ln(64)- \pi}{8}$?

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score 151 · Answer 5 · 2015-01-05 15:01:36

151

Views

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score 312 · Answer 6 · 2026-04-04 04:35:28

312

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score 3.3k · Answer 7 · 2015-01-09 15:48:59

3.3k

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score 53 · Answer 8 · 2026-04-01 09:08:16

53

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score 67 · Answer 9 · 2015-01-12 11:20:29

67

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score 63 · Answer 10 · 2015-01-12 18:56:35

63

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score 44 · Answer 11 · 2015-01-16 16:04:40

44

Views

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score 74 · Answer 12 · 2015-01-16 17:35:21

74

Views

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score 3.7k · Answer 13 · 2026-04-10 20:04:08

3.7k

Views

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Published on 10 Apr 2026 - 20:04

score 41 · Answer 14 · 2015-01-17 15:05:58

41

Views

Uniform convergence $f_n(a) = a^{4n} + \frac1{n^2}$

Published on 17 Jan 2015 - 15:05

score 59 · Answer 15 · 2015-01-17 16:36:03

59

Views

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Published on 17 Jan 2015 - 16:36

List Question

Does $f_n(x):=\left(\frac{n^n}{n!}\prod_{k=1}^n\frac{x+\frac{n}{k}}{x^2+\frac{n^2}{k^2}}\right)^{\frac{x}{n}}$ converge uniformly?

Show that the sequence $(f_n)_{n \in \mathbb{N}} \in (C^0([0,2]),||\cdot||_1)$, is a Cauchy-sequence, but does not converge

Uniform convergence for a "sequence" of functions indexed by a real parameter

How to rigorously prove that $\sum\limits_{n=1}^ \infty( \frac{1}{4n-1} - \frac{1}{4n} )=\frac{\ln(64)- \pi}{8}$?

Uniformly convergent series on $\vert x\vert \leq k$ where $k\in (0,1)$

Proving $\Gamma(x)$ is holomorphic

An extension of a continuous function onto the closure

Uniform convergence of $A^n/n!$

Uniform convergence of series of arccosines

Is this sequence uniformly convergent?

Tell if a series converges uniformly

Uniform convergency of a given sequence of function

Example for a sequence of continuous functions which converge to a continuous function pointwise but not uniformly on a compact set.

Uniform convergence $f_n(a) = a^{4n} + \frac1{n^2}$

Uniform continous functions?

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