Question

Show this function series converge uniformly to a derivative function on $\mathbb{R}$.

score 174 · Answer 1 · 2018-09-05 09:55:36

174

Views

Show this function series converge uniformly to a derivative function on $\mathbb{R}$.

Published on 05 Sep 2018 - 9:55

score 109 · Answer 2 · 2018-09-05 10:29:40

109

Views

Show that $\sum^{\infty}_{n=1}(-1)^{n+1}\frac{1}{n+x^4}$ is uniformly convergent on $\Bbb{R}$

Published on 05 Sep 2018 - 10:29

score 40 · Answer 3 · 2018-09-05 12:26:44

40

Views

Uniform convergence of logarithm on a compact set.

Published on 05 Sep 2018 - 12:26

score 39 · Answer 4 · 2026-03-28 02:24:26

39

Views

If $f(x)=\sum^{\infty}_{n=0}a_n x^n$ converges for $x=50$, can $f$ be uniformly continuous over $[0,10]$?

Published on 28 Mar 2026 - 2:24

score 300 · Answer 5 · 2018-09-07 12:23:39

300

Views

Infinite sum smoothness Proof

Published on 07 Sep 2018 - 12:23

score 16 · Answer 6 · 2018-09-08 15:02:12

16

Views

Convergence of two binomials with equal n as their parameters converge

Published on 08 Sep 2018 - 15:02

score 134 · Answer 7 · 2026-03-25 20:20:28

134

Views

Find region of convergence of double power series

Published on 25 Mar 2026 - 20:20

score 84 · Answer 8 · 2018-09-10 20:51:09

84

Views

Does the series $s_n(x)=\sum^{n}_{k=0}\frac{e^{-kx}}{1+kx}$ converge uniformly over $ [1,2]?$

Published on 10 Sep 2018 - 20:51

score 1.8k · Answer 9 · 2018-09-10 21:23:12

1.8k

Views

If $\{f_n\}$ converges uniformly on $(a,b)$, $\{f_{n}(a)\}$ and $\{f_{n}(b)\}$ converge pointwise, then it converges uniformly on $[a,b]$

Published on 10 Sep 2018 - 21:23

score 573 · Answer 10 · 2018-09-10 21:50:33

573

Views

Uniform Convergence of $\sum_{n=1}^{\infty} \frac{\sin(nx)}{\sqrt{n}}, [0, 2\pi]$ by using Cauchy's test or Weierstrass-M test

Published on 10 Sep 2018 - 21:50

score 601 · Answer 11 · 2018-09-11 10:46:27

601

Views

Prob. 10 (a), Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A Partial Converse To The Uniform Limit Theorem

Published on 11 Sep 2018 - 10:46

score 62 · Answer 12 · 2018-09-11 13:19:38

62

Views

Using definition to show that $x^n$ on [0,1] is not uniform convergent

Published on 11 Sep 2018 - 13:19

score 199 · Answer 13 · 2026-02-23 03:00:00

199

Views

Prove that $f_n(x)=\sin{\sqrt{x+4n^2\pi ^2}}\,,\;x\geq 0$ is equicontinous on $[0,+\infty)$

Published on 23 Feb 2026 - 3:00

score 316 · Answer 14 · 2018-09-14 09:55:55

316

Views

relaxation on Dini's Theorem

Published on 14 Sep 2018 - 9:55

score 2.8k · Answer 15 · 2026-03-23 04:17:36

2.8k

Views

Does $\sum^{\infty}_{n=1}xe^{-nx}$ converge uniformly on $[0,\infty)$?

Published on 23 Mar 2026 - 4:17

List Question

Show this function series converge uniformly to a derivative function on $\mathbb{R}$.

Show that $\sum^{\infty}_{n=1}(-1)^{n+1}\frac{1}{n+x^4}$ is uniformly convergent on $\Bbb{R}$

Uniform convergence of logarithm on a compact set.

If $f(x)=\sum^{\infty}_{n=0}a_n x^n$ converges for $x=50$, can $f$ be uniformly continuous over $[0,10]$?

Infinite sum smoothness Proof

Convergence of two binomials with equal n as their parameters converge

Find region of convergence of double power series

Does the series $s_n(x)=\sum^{n}_{k=0}\frac{e^{-kx}}{1+kx}$ converge uniformly over $ [1,2]?$

If $\{f_n\}$ converges uniformly on $(a,b)$, $\{f_{n}(a)\}$ and $\{f_{n}(b)\}$ converge pointwise, then it converges uniformly on $[a,b]$

Uniform Convergence of $\sum_{n=1}^{\infty} \frac{\sin(nx)}{\sqrt{n}}, [0, 2\pi]$ by using Cauchy's test or Weierstrass-M test

Prob. 10 (a), Sec. 26, in Munkres' TOPOLOGY, 2nd ed: A Partial Converse To The Uniform Limit Theorem

Using definition to show that $x^n$ on [0,1] is not uniform convergent

Prove that $f_n(x)=\sin{\sqrt{x+4n^2\pi ^2}}\,,\;x\geq 0$ is equicontinous on $[0,+\infty)$

relaxation on Dini's Theorem

Does $\sum^{\infty}_{n=1}xe^{-nx}$ converge uniformly on $[0,\infty)$?

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