Question

Sequence of functions and Uniform convergence

score 143 · Answer 1 · 2015-04-24 01:05:26

143

Views

Sequence of functions and Uniform convergence

Published on 24 Apr 2015 - 1:05

score 984 · Answer 2 · 2015-04-26 23:52:31

984

Views

Uniform convergence on compact sets implies interchange of summation and integration

Published on 26 Apr 2015 - 23:52

score 57 · Answer 3 · 2015-04-27 13:02:09

57

Views

How to prove $\frac{nx^3}{1 + n^2 x^2}$ converges uniformly on $[1, \infty)$

Published on 27 Apr 2015 - 13:02

score 17k · Answer 4 · 2015-04-27 13:29:07

17k

Views

Why is $f_n(x) = x^n$ not uniformly convergent on $(0, 1)$?

Published on 27 Apr 2015 - 13:29

score 154 · Answer 5 · 2026-03-31 15:47:21

154

Views

Showing that $P_r(x)=\frac{1-r^2}{1-2r\cos x+r^2}\rightarrow 0$ uniformly on $[-\pi,-\delta]\cup[\delta,\pi]$ as $r\uparrow 1$

Published on 31 Mar 2026 - 15:47

score 490 · Answer 6 · 2015-04-30 00:35:17

490

Views

Non-uniform convergence example

Published on 30 Apr 2015 - 0:35

score 495 · Answer 7 · 2015-05-01 06:16:58

495

Views

Proving uniform convergence of sequence of functions

Published on 01 May 2015 - 6:16

score 210 · Answer 8 · 2015-05-01 19:48:06

210

Views

Uniform convergence, and how to show it?

Published on 01 May 2015 - 19:48

score 69 · Answer 9 · 2015-05-02 19:21:18

69

Views

Convergence of the sequence, $f_{n}(x)$.

Published on 02 May 2015 - 19:21

score 92 · Answer 10 · 2015-05-03 11:06:25

92

Views

Show that $f_n(x)=\frac{1-(x/b)^n}{1+(a/x)^n}$ with $0<a<b,$ and $x \in [a,b]$ is not uniformly convergent

Published on 03 May 2015 - 11:06

score 111 · Answer 11 · 2015-05-03 16:51:16

111

Views

Prove that $f_n(x)=\frac{1-(x/b)^n}{1+(a/x)^n}$ is uniformly convergent on the interval $[a+\epsilon ; b - \epsilon]$

Published on 03 May 2015 - 16:51

score 1.6k · Answer 12 · 2015-05-04 19:00:41

1.6k

Views

Uniform convergence of $\{\tanh(nx)\}_{n=0}^{\infty}$

Published on 04 May 2015 - 19:00

score 534 · Answer 13 · 2026-04-11 20:12:00

534

Views

Pointwise convergence and the convergence of a distribution sequence.

Published on 11 Apr 2026 - 20:12

score 1.2k · Answer 14 · 2015-05-05 23:56:57

1.2k

Views

If K $\subset \mathbb{R}$ is compact prove that ${f_n}$ converges uniformly to f on K.

Published on 05 May 2015 - 23:56

score 224 · Answer 15 · 2015-05-06 16:17:38

224

Views

Uniform convergence of sequence of functions with infinite roots to a limit with finite roots

Published on 06 May 2015 - 16:17

List Question

Sequence of functions and Uniform convergence

Uniform convergence on compact sets implies interchange of summation and integration

How to prove $\frac{nx^3}{1 + n^2 x^2}$ converges uniformly on $[1, \infty)$

Why is $f_n(x) = x^n$ not uniformly convergent on $(0, 1)$?

Showing that $P_r(x)=\frac{1-r^2}{1-2r\cos x+r^2}\rightarrow 0$ uniformly on $[-\pi,-\delta]\cup[\delta,\pi]$ as $r\uparrow 1$

Non-uniform convergence example

Proving uniform convergence of sequence of functions

Uniform convergence, and how to show it?

Convergence of the sequence, $f_{n}(x)$.

Show that $f_n(x)=\frac{1-(x/b)^n}{1+(a/x)^n}$ with $0<a<b,$ and $x \in [a,b]$ is not uniformly convergent

Prove that $f_n(x)=\frac{1-(x/b)^n}{1+(a/x)^n}$ is uniformly convergent on the interval $[a+\epsilon ; b - \epsilon]$

Uniform convergence of $\{\tanh(nx)\}_{n=0}^{\infty}$

Pointwise convergence and the convergence of a distribution sequence.

If K $\subset \mathbb{R}$ is compact prove that ${f_n}$ converges uniformly to f on K.

Uniform convergence of sequence of functions with infinite roots to a limit with finite roots

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