Question

$\int_{[a,b]}^{} f(z) dz = \lim_{n\to\infty} \int_{[a_n,b_n]}^{} f(z)dz $

score 46 · Answer 1 · 2026-04-16 06:11:06

46

Views

$\int_{[a,b]}^{} f(z) dz = \lim_{n\to\infty} \int_{[a_n,b_n]}^{} f(z)dz $

Published on 16 Apr 2026 - 6:11

score 122 · Answer 2 · 2026-04-14 18:04:23

122

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Show that $\sum\limits_{k=1}^{+\infty}[\frac{1}{k}-\frac{1}{k+t}]$ is uniformly-convergent

Published on 14 Apr 2026 - 18:04

score 37 · Answer 3 · 2026-04-14 00:40:45

37

Views

Formulas for pointwise and uniform convergence

Published on 14 Apr 2026 - 0:40

score 874 · Answer 4 · 2026-04-16 03:44:09

874

Views

Uniform convergence of the series $\sum_{n=1}^\infty \frac{1}{n} (\frac{x-1}{x+1})^n$

Published on 16 Apr 2026 - 3:44

score 397 · Answer 5 · 2026-04-17 16:29:02

397

Views

Showing every continuous function $f$ on $[a,b]$ is the uniform limit of a seq of polynomials $(q_{n})$, where $q_{n}(x) = x^{n}p_{n}(x)$

Published on 17 Apr 2026 - 16:29

score 154 · Answer 6 · 2026-04-16 02:37:45

154

Views

The function sequence $(\exp(f_n))$ converges uniformly if the function sequence $(f_n)$ converges uniformly.

Published on 16 Apr 2026 - 2:37

score 41 · Answer 7 · 2026-04-12 00:04:23

41

Views

A series involving spectrum of $- \Delta_{\mathbb{S}^2}$

Published on 12 Apr 2026 - 0:04

score 1k · Answer 8 · 2026-04-15 12:48:57

1k

Views

Does the series $\sum_{n=1}^{\infty}\frac{\cos(n+x)}{n}$ converge uniformly?

Published on 15 Apr 2026 - 12:48

score 450 · Answer 9 · 2026-04-09 16:47:22

450

Views

Conditions for Differentiable Limit Theorem

Published on 09 Apr 2026 - 16:47

score 746 · Answer 10 · 2026-04-13 05:10:10

746

Views

Uniform convergence of $\sum_{n=1}^{\infty} \dfrac{z^{n}}{1+z^{2n}}$

Published on 13 Apr 2026 - 5:10

score 141 · Answer 11 · 2026-04-15 20:26:01

141

Views

Uniform convergence of the power series on $\mathbb R^-$

Published on 15 Apr 2026 - 20:26

score 415 · Answer 12 · 2026-04-15 23:04:48

415

Views

Does $(f_n)=(n\sin(\frac{x}{n})-x)$ converge uniformly on $[-a,a]$ for $a\geq0$?

Published on 15 Apr 2026 - 23:04

score 143 · Answer 13 · 2026-05-10 17:13:42

143

Views

Uniform convergence of expectation and probability

Published on 10 May 2026 - 17:13

score 182 · Answer 14 · 2026-04-11 11:23:36

182

Views

compact convergence on a non-compact metric space implies continuity

Published on 11 Apr 2026 - 11:23

score 131 · Answer 15 · 2026-04-16 09:07:51

131

Views

Uniform convergence of $f_n(x) = \frac{nx}{1+n^2x^2}$ on $[a,\infty), a>0$

Published on 16 Apr 2026 - 9:07

List Question

$\int_{[a,b]}^{} f(z) dz = \lim_{n\to\infty} \int_{[a_n,b_n]}^{} f(z)dz $

Show that $\sum\limits_{k=1}^{+\infty}[\frac{1}{k}-\frac{1}{k+t}]$ is uniformly-convergent

Formulas for pointwise and uniform convergence

Uniform convergence of the series $\sum_{n=1}^\infty \frac{1}{n} (\frac{x-1}{x+1})^n$

Showing every continuous function $f$ on $[a,b]$ is the uniform limit of a seq of polynomials $(q_{n})$, where $q_{n}(x) = x^{n}p_{n}(x)$

The function sequence $(\exp(f_n))$ converges uniformly if the function sequence $(f_n)$ converges uniformly.

A series involving spectrum of $- \Delta_{\mathbb{S}^2}$

Does the series $\sum_{n=1}^{\infty}\frac{\cos(n+x)}{n}$ converge uniformly?

Conditions for Differentiable Limit Theorem

Uniform convergence of $\sum_{n=1}^{\infty} \dfrac{z^{n}}{1+z^{2n}}$

Uniform convergence of the power series on $\mathbb R^-$

Does $(f_n)=(n\sin(\frac{x}{n})-x)$ converge uniformly on $[-a,a]$ for $a\geq0$?

Uniform convergence of expectation and probability

compact convergence on a non-compact metric space implies continuity

Uniform convergence of $f_n(x) = \frac{nx}{1+n^2x^2}$ on $[a,\infty), a>0$

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