Question

Uniform convergence of $f_n= \frac{nxe^{-nx}}{n^2x^2+1}$

score 210 · Answer 1 · 2020-05-21 19:52:31

210

Views

Uniform convergence of $f_n= \frac{nxe^{-nx}}{n^2x^2+1}$

Published on 21 May 2020 - 19:52

score 53 · Answer 2 · 2020-05-21 22:09:23

53

Views

How do we prove that a power series centered at $a\in\textbf{R}$ is continuous on the interval $(a-R,a+R)$?

Published on 21 May 2020 - 22:09

score 75 · Answer 3 · 2020-05-22 09:15:54

75

Views

$\frac{n}{2}\int_{x-1/n}^{x+1/n} f(t)dt$ converges uniformly to $f$ where $f:\Bbb R\to \Bbb R$ is continuous

Published on 22 May 2020 - 9:15

score 105 · Answer 4 · 2020-05-22 09:33:49

105

Views

Termwise differentiation of series

Published on 22 May 2020 - 9:33

score 36 · Answer 5 · 2020-05-22 12:53:04

36

Views

prove that $\lim_{n\to\infty} \int_a^b |f(x) - f_n(x)|^p dx =0$ for every $p>0$

Published on 22 May 2020 - 12:53

score 41 · Answer 6 · 2020-05-22 14:57:16

41

Views

$f_n$ uniform converge to f in $[a,b)$ means it uniform converge in $[a,b]$?

Published on 22 May 2020 - 14:57

score 37 · Answer 7 · 2020-05-22 22:10:46

37

Views

Uniform converge, using the Supremum theorem (want to make sure I solved correctly)

Published on 22 May 2020 - 22:10

score 390 · Answer 8 · 2026-02-24 16:05:25

390

Views

Dini's theorem (specific case)

Published on 24 Feb 2026 - 16:05

score 172 · Answer 9 · 2020-05-23 19:11:06

172

Views

Uniform convergence of $f_n(z)=nz^n$ in the set $|z|<\frac{1}{2}$

Published on 23 May 2020 - 19:11

score 33 · Answer 10 · 2026-04-04 16:57:04

33

Views

Argue for or against that the Fourier series for $f(x) = 6x+2$ converges uniformly and/or uniformly

Published on 04 Apr 2026 - 16:57

score 118 · Answer 11 · 2020-05-23 22:01:10

118

Views

Proving that $f_n(z)=nz^n$ converges uniformly for $|z|<\frac{1}{2}$.

Published on 23 May 2020 - 22:01

score 81 · Answer 12 · 2020-05-23 23:25:46

81

Views

Prove $\lim_{n \to \infty} (1 + z/n)^n$ does NOT converge uniformly on $\mathbb{C}$

Published on 23 May 2020 - 23:25

score 31 · Answer 13 · 2020-05-24 06:15:38

31

Views

A small doubt related to Uniform convergence

Published on 24 May 2020 - 6:15

score 118 · Answer 14 · 2020-05-24 20:59:21

118

Views

Uniform convergence of $\sum_{k=2}^{\infty}\left(\cos\frac{x}{k}-\cos\frac{x}{k-1}\right)$

Published on 24 May 2020 - 20:59

score 62 · Answer 15 · 2026-03-27 07:13:35

62

Views

Are there references about universal power series and this statement?

Published on 27 Mar 2026 - 7:13

List Question

Uniform convergence of $f_n= \frac{nxe^{-nx}}{n^2x^2+1}$

How do we prove that a power series centered at $a\in\textbf{R}$ is continuous on the interval $(a-R,a+R)$?

$\frac{n}{2}\int_{x-1/n}^{x+1/n} f(t)dt$ converges uniformly to $f$ where $f:\Bbb R\to \Bbb R$ is continuous

Termwise differentiation of series

prove that $\lim_{n\to\infty} \int_a^b |f(x) - f_n(x)|^p dx =0$ for every $p>0$

$f_n$ uniform converge to f in $[a,b)$ means it uniform converge in $[a,b]$?

Uniform converge, using the Supremum theorem (want to make sure I solved correctly)

Dini's theorem (specific case)

Uniform convergence of $f_n(z)=nz^n$ in the set $|z|<\frac{1}{2}$

Argue for or against that the Fourier series for $f(x) = 6x+2$ converges uniformly and/or uniformly

Proving that $f_n(z)=nz^n$ converges uniformly for $|z|<\frac{1}{2}$.

Prove $\lim_{n \to \infty} (1 + z/n)^n$ does NOT converge uniformly on $\mathbb{C}$

A small doubt related to Uniform convergence

Uniform convergence of $\sum_{k=2}^{\infty}\left(\cos\frac{x}{k}-\cos\frac{x}{k-1}\right)$

Are there references about universal power series and this statement?

Trending Questions

Popular # Hahtags

Popular Questions