Question

If a power series converges uniformly on $\mathbb{R}$ then it must be to $0$?

score 1.2k · Answer 1 · 2015-01-27 18:40:26

1.2k

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If a power series converges uniformly on $\mathbb{R}$ then it must be to $0$?

Published on 27 Jan 2015 - 18:40

score 197 · Answer 2 · 2015-01-28 14:13:27

197

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Uniform Convergence of Series $\sum_{n=1}^{\infty}\frac{\sin(x)^n}{n}$

Published on 28 Jan 2015 - 14:13

score 378 · Answer 3 · 2015-01-28 20:48:11

378

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Prove that $\lim_{n \rightarrow \infty} \int_0^1 f_n(x)dx \ne \int_0^1\lim_{n \rightarrow \infty}f_n(x) dx$

Published on 28 Jan 2015 - 20:48

score 63 · Answer 4 · 2015-01-29 11:46:42

Prove that if $f_n \to f$ uniformly on all closed intervals $[c,d] \subset (a,b)$, then $f_ng\to fg$ uniformly on $[a,b]$

score 118 · Answer 5 · 2015-01-29 17:59:52

118

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Prove that $f_n(x) = \left(\frac{x}{n}\right)^ne^{-x}$ converges uniformly

Published on 29 Jan 2015 - 17:59

score 111 · Answer 6 · 2015-01-30 13:40:31

111

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For which $\alpha > 0$ we can interchange the integral with the summation?

Published on 30 Jan 2015 - 13:40

score 257 · Answer 7 · 2015-01-31 12:02:44

257

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Prove $f(x) = \sum_{n=1}^\infty \frac{\sin nx + \cos nx}{n^3}$ is well-defined and $C^1$.

Published on 31 Jan 2015 - 12:02

score 95 · Answer 8 · 2026-04-03 02:37:49

95

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Convergence of series of integrals

Published on 03 Apr 2026 - 2:37

score 3.8k · Answer 9 · 2015-02-03 18:33:28

3.8k

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Uniform limit of analytic functions

Published on 03 Feb 2015 - 18:33

score 623 · Answer 10 · 2015-02-04 12:32:51

623

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uniform convergence of a function series and related series sum

Published on 04 Feb 2015 - 12:32

score 1.2k · Answer 11 · 2015-02-05 09:55:47

1.2k

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If $f_j$ converges uniformly to $f$, does $\frac{1}{f_j}$ converge uniformly to $\frac{1}{f}$?

Published on 05 Feb 2015 - 9:55

score 265 · Answer 12 · 2026-04-10 21:44:55

265

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Application of Stone Weierstrass theorem

Published on 10 Apr 2026 - 21:44

score 64 · Answer 13 · 2026-04-11 00:49:45

64

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How do I show that this function is increasing, and has discontinuities at points in this sequence

Published on 11 Apr 2026 - 0:49

score 606 · Answer 14 · 2015-02-08 21:13:21

606

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Question about the $M$ value in Weierstrass $M$-test

Published on 08 Feb 2015 - 21:13

score 411 · Answer 15 · 2015-02-09 04:45:45

411

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Clarification on Pointwise and Uniform convergence

Published on 09 Feb 2015 - 4:45

List Question

If a power series converges uniformly on $\mathbb{R}$ then it must be to $0$?

Uniform Convergence of Series $\sum_{n=1}^{\infty}\frac{\sin(x)^n}{n}$

Prove that $\lim_{n \rightarrow \infty} \int_0^1 f_n(x)dx \ne \int_0^1\lim_{n \rightarrow \infty}f_n(x) dx$

Prove that if $f_n \to f$ uniformly on all closed intervals $[c,d] \subset (a,b)$, then $f_ng\to fg$ uniformly on $[a,b]$

Prove that $f_n(x) = \left(\frac{x}{n}\right)^ne^{-x}$ converges uniformly

For which $\alpha > 0$ we can interchange the integral with the summation?

Prove $f(x) = \sum_{n=1}^\infty \frac{\sin nx + \cos nx}{n^3}$ is well-defined and $C^1$.

Convergence of series of integrals

Uniform limit of analytic functions

uniform convergence of a function series and related series sum

If $f_j$ converges uniformly to $f$, does $\frac{1}{f_j}$ converge uniformly to $\frac{1}{f}$?

Application of Stone Weierstrass theorem

How do I show that this function is increasing, and has discontinuities at points in this sequence

Question about the $M$ value in Weierstrass $M$-test

Clarification on Pointwise and Uniform convergence

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