Question

Show uniform convergence of the series of functions $\sum_{n=1}^\infty \frac{x^n \sin(nx)}{n}$

score 885 · Answer 1 · 2026-04-17 15:15:16

885

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Show uniform convergence of the series of functions $\sum_{n=1}^\infty \frac{x^n \sin(nx)}{n}$

Published on 17 Apr 2026 - 15:15

score 4.9k · Answer 2 · 2026-04-09 15:39:08

4.9k

Views

What are the applications of sequence of functions?

Published on 09 Apr 2026 - 15:39

score 331 · Answer 3 · 2026-04-15 23:12:26

331

Views

Pointwise and uniform convergence of $\sum_{n=1}^{+\infty}\big({\frac{x}{1+x^n}}\big)^n$

Published on 15 Apr 2026 - 23:12

score 63 · Answer 4 · 2026-04-16 08:36:28

63

Views

Prove that $f(\alpha)$ is differentiable using uniform convergence.

Published on 16 Apr 2026 - 8:36

score 35 · Answer 5 · 2026-04-16 00:05:28

35

Views

Do we have $\lim_{r\to\infty}\frac{1}{r}\int_{-r}^r\left(\sup_{x-1\leq\theta\leq x}|f(\theta)|\right)dx=0$?

Published on 16 Apr 2026 - 0:05

score 107 · Answer 6 · 2026-04-17 09:11:39

107

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Uniform convergence of $\int_0^{+\infty}\frac{1-\cos{\alpha x}}{x}e^{-\lambda x}dx$

Published on 17 Apr 2026 - 9:11

score 98 · Answer 7 · 2026-04-11 02:30:26

98

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Discontinuity of a series of continuous functions

Published on 11 Apr 2026 - 2:30

score 29 · Answer 8 · 2026-04-16 13:29:27

29

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Given $\sum_{k\geq 0} f_k,\quad(f_k(x) :=\sin^k(x)),$ on what $I\subset\mathbb{R}$ does this converge uniformly to a limit function $g$?

Published on 16 Apr 2026 - 13:29

score 136 · Answer 9 · 2026-04-15 23:34:41

136

Views

Prove that the series $\sum_{n=1}^{\infty}\int_{n}^{n+1}(\frac{1}{n^z} - \frac{1}{x^z})dx$ converges uniformly on $\mathbb{C}_{\epsilon}$

Published on 15 Apr 2026 - 23:34

score 52 · Answer 10 · 2026-04-17 08:58:36

52

Views

Pointwise/uniform convergence of $ f(x) = \begin{cases} +\infty, & \text{if }0<x<0 \text{ (???)}\\ 1, & \text{if }1/(2n)≤x<1 \end{cases} $

Published on 17 Apr 2026 - 8:58

score 398 · Answer 11 · 2026-04-16 12:03:36

398

Views

Uniform convergence of $n\sin\sqrt{4\pi^2n^2+x^2}$ on $[0,a]$ and $\mathbb{R}.$

Published on 16 Apr 2026 - 12:03

score 6.5k · Answer 12 · 2026-04-13 17:04:01

6.5k

Views

Is the uniform limit of uniformly continuous functions, uniformly continuous itself?

Published on 13 Apr 2026 - 17:04

score 128 · Answer 13 · 2026-04-17 15:20:19

128

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Studying uniform convergence of function sequence $f_n=\frac{n}{n^2+x^2}$ and $f_n=\frac{x^n}{1+x^n}$

Published on 17 Apr 2026 - 15:20

score 248 · Answer 14 · 2026-04-13 04:10:30

248

Views

Uniform convergence of a function series over an open interval.

Published on 13 Apr 2026 - 4:10

score 8.2k · Answer 15 · 2026-04-16 10:06:02

8.2k

Views

Convergence of Series $\sum 1/(1+ n^2 x)$ Uniformly (Homework)

Published on 16 Apr 2026 - 10:06

List Question

Show uniform convergence of the series of functions $\sum_{n=1}^\infty \frac{x^n \sin(nx)}{n}$

What are the applications of sequence of functions?

Pointwise and uniform convergence of $\sum_{n=1}^{+\infty}\big({\frac{x}{1+x^n}}\big)^n$

Prove that $f(\alpha)$ is differentiable using uniform convergence.

Do we have $\lim_{r\to\infty}\frac{1}{r}\int_{-r}^r\left(\sup_{x-1\leq\theta\leq x}|f(\theta)|\right)dx=0$?

Uniform convergence of $\int_0^{+\infty}\frac{1-\cos{\alpha x}}{x}e^{-\lambda x}dx$

Discontinuity of a series of continuous functions

Given $\sum_{k\geq 0} f_k,\quad(f_k(x) :=\sin^k(x)),$ on what $I\subset\mathbb{R}$ does this converge uniformly to a limit function $g$?

Prove that the series $\sum_{n=1}^{\infty}\int_{n}^{n+1}(\frac{1}{n^z} - \frac{1}{x^z})dx$ converges uniformly on $\mathbb{C}_{\epsilon}$

Pointwise/uniform convergence of $ f(x) = \begin{cases} +\infty, & \text{if }0<x<0 \text{ (???)}\\ 1, & \text{if }1/(2n)≤x<1 \end{cases} $

Uniform convergence of $n\sin\sqrt{4\pi^2n^2+x^2}$ on $[0,a]$ and $\mathbb{R}.$

Is the uniform limit of uniformly continuous functions, uniformly continuous itself?

Studying uniform convergence of function sequence $f_n=\frac{n}{n^2+x^2}$ and $f_n=\frac{x^n}{1+x^n}$

Uniform convergence of a function series over an open interval.

Convergence of Series $\sum 1/(1+ n^2 x)$ Uniformly (Homework)

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