Question

Is this uniformly convergent: $\sum_{k=1}^{\infty} \frac{1}{1+k^2x^2}$ where $x \in (0,1)$?

score 56 · Answer 1 · 2026-04-14 08:03:23

56

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Is this uniformly convergent: $\sum_{k=1}^{\infty} \frac{1}{1+k^2x^2}$ where $x \in (0,1)$?

Published on 14 Apr 2026 - 8:03

score 161 · Answer 2 · 2026-04-14 03:55:30

161

Views

Uniform convergence theorem fails when |E| =$\infty$

Published on 14 Apr 2026 - 3:55

score 35 · Answer 3 · 2026-04-15 04:53:38

35

Views

Uniform convergence of a partial when we have uniform acotation but no equicotinuity

Published on 15 Apr 2026 - 4:53

score 774 · Answer 4 · 2026-04-16 14:24:33

774

Views

find all intervals of uniform convergence

Published on 16 Apr 2026 - 14:24

score 691 · Answer 5 · 2026-04-12 20:33:40

691

Views

Counter example to Stone Weierstrass Theorem

Published on 12 Apr 2026 - 20:33

score 35 · Answer 6 · 2026-04-15 11:51:17

35

Views

Uniform limit depending of analytique functions

Published on 15 Apr 2026 - 11:51

score 123 · Answer 7 · 2026-04-11 17:11:10

123

Views

Strong convergence + convergence of norms -> norm convergence?

Published on 11 Apr 2026 - 17:11

score 1.4k · Answer 8 · 2026-04-16 13:11:15

1.4k

Views

The series $\sum_{n=1}^\infty x(1-x)^n$ is not uniformly convergent on $[0,1]$

Published on 16 Apr 2026 - 13:11

score 1k · Answer 9 · 2026-04-13 20:33:05

1k

Views

Show that a series is not uniformly convergent

Published on 13 Apr 2026 - 20:33

score 204 · Answer 10 · 2026-04-14 22:35:16

204

Views

Pointwise convergence V.S. Uniform convergence

Published on 14 Apr 2026 - 22:35

score 145 · Answer 11 · 2026-04-14 15:08:47

145

Views

A sequence of function $\{f_n\}$ that converges to $f$ point-wise almost everywhere

Published on 14 Apr 2026 - 15:08

score 1.3k · Answer 12 · 2026-04-12 19:02:16

1.3k

Views

Is there any graphical methods by which we can directly notice whether the $\{f_k\}$ converges uniformly?

Published on 12 Apr 2026 - 19:02

score 2k · Answer 13 · 2026-04-12 00:46:30

2k

Views

Intuition about the Bernstein polynomials proof of the Weierstrass approximation theorem

Published on 12 Apr 2026 - 0:46

score 464 · Answer 14 · 2026-04-14 12:04:29

464

Views

Uniform limit of a sequence of bounded derivatives is a bounded derivative?

Published on 14 Apr 2026 - 12:04

score 321 · Answer 15 · 2026-04-12 03:27:43

321

Views

Is there a sandwich method for uniform convergence?

Published on 12 Apr 2026 - 3:27

List Question

Is this uniformly convergent: $\sum_{k=1}^{\infty} \frac{1}{1+k^2x^2}$ where $x \in (0,1)$?

Uniform convergence theorem fails when |E| =$\infty$

Uniform convergence of a partial when we have uniform acotation but no equicotinuity

find all intervals of uniform convergence

Counter example to Stone Weierstrass Theorem

Uniform limit depending of analytique functions

Strong convergence + convergence of norms -> norm convergence?

The series $\sum_{n=1}^\infty x(1-x)^n$ is not uniformly convergent on $[0,1]$

Show that a series is not uniformly convergent

Pointwise convergence V.S. Uniform convergence

A sequence of function $\{f_n\}$ that converges to $f$ point-wise almost everywhere

Is there any graphical methods by which we can directly notice whether the $\{f_k\}$ converges uniformly?

Intuition about the Bernstein polynomials proof of the Weierstrass approximation theorem

Uniform limit of a sequence of bounded derivatives is a bounded derivative?

Is there a sandwich method for uniform convergence?

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