Question

Uniformly convergent and Weierstrass M-test

score 311 · Answer 1 · 2026-04-01 19:07:14

311

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Uniformly convergent and Weierstrass M-test

Published on 01 Apr 2026 - 19:07

score 75 · Answer 2 · 2026-04-02 19:13:24

75

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Completeness of $B(X,R)$

Published on 02 Apr 2026 - 19:13

score 323 · Answer 3 · 2026-03-30 00:19:16

323

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Uniform convergence from pointwise convergence for uniform Lipshitz functions

Published on 30 Mar 2026 - 0:19

score 71 · Answer 4 · 2015-11-22 14:44:36

71

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Prove that for any $x>1$, $\lim_{n \to \infty} \int_0^n t^{x-1}(1-\frac{t}{n})^n dt = \Gamma(x)$

Published on 22 Nov 2015 - 14:44

score 97 · Answer 5 · 2015-11-22 16:46:41

97

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On a series of functions exercise: $\sum_{n=1}^{\infty} n \ln (1+ \frac{|\sin x|^n}{1+|x|^n})$.

Published on 22 Nov 2015 - 16:46

score 146 · Answer 6 · 2015-11-22 20:00:31

146

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Non-Power Series Examples of Uniform Convergence

Published on 22 Nov 2015 - 20:00

score 661 · Answer 7 · 2015-11-22 23:29:19

661

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Cauchy Criterion - Prove $\sum_{k=1}^{\infty}(-1)^{k-1}\frac{x^k}{\sqrt k}$ converges uniformly on $[0,1]$

Published on 22 Nov 2015 - 23:29

score 243 · Answer 8 · 2026-04-10 21:56:23

243

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Can I avoid the Abel partial summation technique and instead prove uniform convergence in this way?

Published on 10 Apr 2026 - 21:56

score 76 · Answer 9 · 2026-04-13 00:03:11

76

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Convergence and sum of $\sum_{n=0}^\infty \frac{x}{(2nx-x+1)(2nx+x+1)}$

Published on 13 Apr 2026 - 0:03

score 327 · Answer 10 · 2026-04-12 05:41:30

327

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Series Uniform Convergence Question

Published on 12 Apr 2026 - 5:41

score 57 · Answer 11 · 2015-11-24 10:10:52

57

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Uniform convergence of ${f_n(x)=\int_{0}^{x}g_n(t)}dt$ where $g_n(x)=\sin^2(x+\frac{1}{n})$.

Published on 24 Nov 2015 - 10:10

score 151 · Answer 12 · 2026-03-30 00:22:42

151

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(dis)prove:$\sup_{F \in 2^{(L^1(S,\mathbb{R}))}}\limsup\sup_{f\in F}|\int f dP_n-\int fdP|=\limsup\sup_{f\in L^1(S,\mathbb{R})}|\int fdP_n-\int fdP|$

Published on 30 Mar 2026 - 0:22

score 1.4k · Answer 13 · 2015-11-25 16:24:38

1.4k

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Does $\sum \frac{\sin^2(nx)}{n^2x}$ converges uniformly on $(0,\delta]$?

Published on 25 Nov 2015 - 16:24

score 68 · Answer 14 · 2015-11-28 09:40:16

68

Views

Proving differentiability on every interval equals proving differentiability on all of $\mathbb{R}$?

Published on 28 Nov 2015 - 9:40

score 779 · Answer 15 · 2015-11-28 20:11:25

779

Views

Weak convergence implies uniform convergence

Published on 28 Nov 2015 - 20:11

List Question

Uniformly convergent and Weierstrass M-test

Completeness of $B(X,R)$

Uniform convergence from pointwise convergence for uniform Lipshitz functions

Prove that for any $x>1$, $\lim_{n \to \infty} \int_0^n t^{x-1}(1-\frac{t}{n})^n dt = \Gamma(x)$

On a series of functions exercise: $\sum_{n=1}^{\infty} n \ln (1+ \frac{|\sin x|^n}{1+|x|^n})$.

Non-Power Series Examples of Uniform Convergence

Cauchy Criterion - Prove $\sum_{k=1}^{\infty}(-1)^{k-1}\frac{x^k}{\sqrt k}$ converges uniformly on $[0,1]$

Can I avoid the Abel partial summation technique and instead prove uniform convergence in this way?

Convergence and sum of $\sum_{n=0}^\infty \frac{x}{(2nx-x+1)(2nx+x+1)}$

Series Uniform Convergence Question

Uniform convergence of ${f_n(x)=\int_{0}^{x}g_n(t)}dt$ where $g_n(x)=\sin^2(x+\frac{1}{n})$.

(dis)prove:$\sup_{F \in 2^{(L^1(S,\mathbb{R}))}}\limsup\sup_{f\in F}|\int f dP_n-\int fdP|=\limsup\sup_{f\in L^1(S,\mathbb{R})}|\int fdP_n-\int fdP|$

Does $\sum \frac{\sin^2(nx)}{n^2x}$ converges uniformly on $(0,\delta]$?

Proving differentiability on every interval equals proving differentiability on all of $\mathbb{R}$?

Weak convergence implies uniform convergence

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