Question

Convergence of $h_{n}(x) = x^{ 1 +\frac{1}{2n-1} }$ defined on [-1,1]

score 49 · Answer 1 · 2026-03-23 12:08:24

49

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Convergence of $h_{n}(x) = x^{ 1 +\frac{1}{2n-1} }$ defined on [-1,1]

Published on 23 Mar 2026 - 12:08

score 78 · Answer 2 · 2018-08-17 07:55:59

78

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Exchange of limit and sum for a uniformly convergent sequence

Published on 17 Aug 2018 - 7:55

score 61 · Answer 3 · 2018-08-18 19:49:24

61

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Is $f_{n}\left(x\right)=\sin\left(x+\frac{x^{2}}{n}\right)$ uniformly convergent on $\left[0,\:2\pi\right]$

Published on 18 Aug 2018 - 19:49

score 147 · Answer 4 · 2018-08-18 21:06:31

147

Views

Why $\sum_{n=1}^{\infty}\frac{n\left(\sin x\right)^{n}}{2+n^{2}}$ is not uniformly convergent on $[0,\;\frac{\pi}{2})$?

Published on 18 Aug 2018 - 21:06

score 34 · Answer 5 · 2018-08-19 12:42:56

34

Views

Show uniform convergence of series with |x|

Published on 19 Aug 2018 - 12:42

score 103 · Answer 6 · 2018-08-19 22:45:47

103

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Can we apply Egorov's theorem?

Published on 19 Aug 2018 - 22:45

score 126 · Answer 7 · 2026-03-26 04:14:34

126

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Uniform convergence and series of expansion

Published on 26 Mar 2026 - 4:14

score 518 · Answer 8 · 2018-08-22 07:38:04

518

Views

Understanding uniform convergence of sequence

Published on 22 Aug 2018 - 7:38

score 99 · Answer 9 · 2018-08-22 15:44:47

99

Views

Check proof that $\int _{-\pi}^\pi\sum\limits_{n=2}^\infty\tan(x/2^n)\mathrm dx=\sum\limits_{n=2}^\infty\int_{-\pi}^\pi\tan(x/2^n)\mathrm dx$

Published on 22 Aug 2018 - 15:44

score 343 · Answer 10 · 2018-08-29 21:25:27

343

Views

Uniform Convergence Example

Published on 29 Aug 2018 - 21:25

score 60 · Answer 11 · 2018-08-31 12:11:07

60

Views

Prove that $t\mapsto \frac{d}{dt}\left[\rho(t)\right]^{-1}=-\rho(t)^{-1}\rho'(t)\rho(t)^{-1}$

Published on 31 Aug 2018 - 12:11

score 483 · Answer 12 · 2026-02-23 06:35:39

483

Views

Differentiability and Uniform convergence on unbounded intervals

Published on 23 Feb 2026 - 6:35

score 474 · Answer 13 · 2026-02-23 06:36:30

474

Views

Determine whether a sequence of functions converges uniformly

Published on 23 Feb 2026 - 6:36

score 319 · Answer 14 · 2026-03-25 17:24:55

319

Views

Uniform convergence of convolution of a distribution with a test function

Published on 25 Mar 2026 - 17:24

score 75 · Answer 15 · 2026-03-28 02:24:26

75

Views

Prove that $x\mapsto \sum^{\infty}_{n=0}f_n(x)=\sum^{\infty}_{n=0}\frac{x^2}{(1+x^2)^n}$ does not converge uniformly on $[-1,1]$

Published on 28 Mar 2026 - 2:24

List Question

Convergence of $h_{n}(x) = x^{ 1 +\frac{1}{2n-1} }$ defined on [-1,1]

Exchange of limit and sum for a uniformly convergent sequence

Is $f_{n}\left(x\right)=\sin\left(x+\frac{x^{2}}{n}\right)$ uniformly convergent on $\left[0,\:2\pi\right]$

Why $\sum_{n=1}^{\infty}\frac{n\left(\sin x\right)^{n}}{2+n^{2}}$ is not uniformly convergent on $[0,\;\frac{\pi}{2})$?

Show uniform convergence of series with |x|

Can we apply Egorov's theorem?

Uniform convergence and series of expansion

Understanding uniform convergence of sequence

Check proof that $\int _{-\pi}^\pi\sum\limits_{n=2}^\infty\tan(x/2^n)\mathrm dx=\sum\limits_{n=2}^\infty\int_{-\pi}^\pi\tan(x/2^n)\mathrm dx$

Uniform Convergence Example

Prove that $t\mapsto \frac{d}{dt}\left[\rho(t)\right]^{-1}=-\rho(t)^{-1}\rho'(t)\rho(t)^{-1}$

Differentiability and Uniform convergence on unbounded intervals

Determine whether a sequence of functions converges uniformly

Uniform convergence of convolution of a distribution with a test function

Prove that $x\mapsto \sum^{\infty}_{n=0}f_n(x)=\sum^{\infty}_{n=0}\frac{x^2}{(1+x^2)^n}$ does not converge uniformly on $[-1,1]$

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