Question

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

score 50 · Answer 1 · 2026-04-09 15:24:39

50

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

Published on 09 Apr 2026 - 15:24

score 81 · Answer 2 · 2026-04-14 03:43:45

81

Views

Exchange of limit and sum for a uniformly convergent sequence

Published on 14 Apr 2026 - 3:43

score 64 · Answer 3 · 2026-04-17 02:25:11

64

Views

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

Published on 17 Apr 2026 - 2:25

score 150 · Answer 4 · 2026-04-15 04:20:48

150

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 15 Apr 2026 - 4:20

score 37 · Answer 5 · 2026-04-14 18:49:50

37

Views

Show uniform convergence of series with |x|

Published on 14 Apr 2026 - 18:49

score 106 · Answer 6 · 2026-04-11 08:53:03

106

Views

Can we apply Egorov's theorem?

Published on 11 Apr 2026 - 8:53

score 128 · Answer 7 · 2026-04-15 14:22:36

128

Views

Uniform convergence and series of expansion

Published on 15 Apr 2026 - 14:22

score 521 · Answer 8 · 2026-04-16 05:40:35

521

Views

Understanding uniform convergence of sequence

Published on 16 Apr 2026 - 5:40

score 102 · Answer 9 · 2026-04-16 06:16:19

102

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 16 Apr 2026 - 6:16

score 346 · Answer 10 · 2026-04-14 03:55:17

346

Views

Uniform Convergence Example

Published on 14 Apr 2026 - 3:55

score 63 · Answer 11 · 2026-04-16 06:16:27

63

Views

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

Published on 16 Apr 2026 - 6:16

score 486 · Answer 12 · 2026-04-13 01:02:31

486

Views

Differentiability and Uniform convergence on unbounded intervals

Published on 13 Apr 2026 - 1:02

score 477 · Answer 13 · 2026-04-13 22:53:47

477

Views

Determine whether a sequence of functions converges uniformly

Published on 13 Apr 2026 - 22:53

score 321 · Answer 14 · 2026-04-14 09:27:38

321

Views

Uniform convergence of convolution of a distribution with a test function

Published on 14 Apr 2026 - 9:27

score 77 · Answer 15 · 2026-04-16 01:28:22

77

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 16 Apr 2026 - 1:28

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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