Question

Show the series $\sum_{n=1}^\infty \frac{z^2}{(1+z^2)^n}$ converges uniformly on $|z^2+1|\geq r>1$

score 50 · Answer 1 · 2026-04-16 15:39:26

50

Views

Show the series $\sum_{n=1}^\infty \frac{z^2}{(1+z^2)^n}$ converges uniformly on $|z^2+1|\geq r>1$

Published on 16 Apr 2026 - 15:39

score 166 · Answer 2 · 2026-04-14 01:05:25

166

Views

Does $\exp{(f_n)}$ converge to $\exp{(f)}$ uniformly if $f_n$ converges to $f$ uniformly?

Published on 14 Apr 2026 - 1:05

score 319 · Answer 3 · 2026-04-15 18:07:09

319

Views

Uniform convergence and Schwartz space

Published on 15 Apr 2026 - 18:07

score 101 · Answer 4 · 2026-04-16 04:34:39

101

Views

Find sets on which $\sum^{\infty}_{n=1} \frac{\cos(nx)}{e^{nx}}$ is uniformly convergent.

Published on 16 Apr 2026 - 4:34

score 168 · Answer 5 · 2026-04-16 23:15:30

168

Views

Convergence of a power series at an endpoint

Published on 16 Apr 2026 - 23:15

score 57 · Answer 6 · 2026-04-16 23:07:05

57

Views

Uniform and pointwise convergence of function series.

Published on 16 Apr 2026 - 23:07

score 54 · Answer 7 · 2026-04-15 04:53:54

54

Views

Uniform convergence of the given series

Published on 15 Apr 2026 - 4:53

score 134 · Answer 8 · 2026-04-15 10:32:04

134

Views

Uniform convergence of $\sum_{n=1}^\infty \frac{1}{z^n+1}$

Published on 15 Apr 2026 - 10:32

score 51 · Answer 9 · 2026-04-16 08:40:22

51

Views

Uniform convergence of $x^n \sin(\frac{1-x}{x})$ on (0,1)$?

Published on 16 Apr 2026 - 8:40

score 86 · Answer 10 · 2026-04-15 08:51:13

86

Views

Uniform convergence of $\sum_{n = 1}^\infty x \sin \frac{1}{(x n)^2}$ on $(0, 1)$.

Published on 15 Apr 2026 - 8:51

score 473 · Answer 11 · 2026-04-11 06:40:04

473

Views

$\sum \frac{z^k}{k}$ does not converge uniformly on $|z|<1$

Published on 11 Apr 2026 - 6:40

score 52 · Answer 12 · 2026-04-15 19:26:08

52

Views

Show that $f_n(x)=n(f(x+\frac{1}{n})-f(x))\to f'$ uniformly (with $f \in C^2$ and $f''$ bounded)

Published on 15 Apr 2026 - 19:26

score 98 · Answer 13 · 2026-04-15 15:57:09

98

Views

Integral of uniformly convergent functions that are monotone and improper integrable

Published on 15 Apr 2026 - 15:57

score 271 · Answer 14 · 2026-04-16 12:03:12

271

Views

Uniform Continuity and Inverse

Published on 16 Apr 2026 - 12:03

score 22 · Answer 15 · 2026-04-17 09:53:33

22

Views

$F_n(t,x)=F(t,x,\lambda_n)$ converges uniformly to $F_0(t,x)=F(t,x,\lambda_0)$ on compacts if $F$ is continuous and $\lambda_n\rightarrow \lambda$

Published on 17 Apr 2026 - 9:53

List Question

Show the series $\sum_{n=1}^\infty \frac{z^2}{(1+z^2)^n}$ converges uniformly on $|z^2+1|\geq r>1$

Does $\exp{(f_n)}$ converge to $\exp{(f)}$ uniformly if $f_n$ converges to $f$ uniformly?

Uniform convergence and Schwartz space

Find sets on which $\sum^{\infty}_{n=1} \frac{\cos(nx)}{e^{nx}}$ is uniformly convergent.

Convergence of a power series at an endpoint

Uniform and pointwise convergence of function series.

Uniform convergence of the given series

Uniform convergence of $\sum_{n=1}^\infty \frac{1}{z^n+1}$

Uniform convergence of $x^n \sin(\frac{1-x}{x})$ on (0,1)$?

Uniform convergence of $\sum_{n = 1}^\infty x \sin \frac{1}{(x n)^2}$ on $(0, 1)$.

$\sum \frac{z^k}{k}$ does not converge uniformly on $|z|<1$

Show that $f_n(x)=n(f(x+\frac{1}{n})-f(x))\to f'$ uniformly (with $f \in C^2$ and $f''$ bounded)

Integral of uniformly convergent functions that are monotone and improper integrable

Uniform Continuity and Inverse

$F_n(t,x)=F(t,x,\lambda_n)$ converges uniformly to $F_0(t,x)=F(t,x,\lambda_0)$ on compacts if $F$ is continuous and $\lambda_n\rightarrow \lambda$

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