Question

Is the improper Dirichlet integral of $\sin(ax)/x$ from $0$ to infinity uniformly convergent?

score 705 · Answer 1 · 2020-04-16 16:45:36

705

Views

Is the improper Dirichlet integral of $\sin(ax)/x$ from $0$ to infinity uniformly convergent?

Published on 16 Apr 2020 - 16:45

score 40 · Answer 2 · 2020-04-17 05:03:26

40

Views

Proving Continuity of power series at $x=1$

Published on 17 Apr 2020 - 5:03

score 33 · Answer 3 · 2026-02-23 14:13:17

33

Views

Let $B_nx=x(t-\frac{1}{n})\in L^2(\mathbb{R})$. Show that $B_n\overset{s}{\to}Id$ but $B_n\not\rightrightarrows Id$

Published on 23 Feb 2026 - 14:13

score 89 · Answer 4 · 2026-02-24 12:35:32

89

Views

Limits under integrals and uniform convergence.

Published on 24 Feb 2026 - 12:35

score 79 · Answer 5 · 2020-04-17 20:17:08

79

Views

I don't understand why we can just extend the domain of this function

Published on 17 Apr 2020 - 20:17

score 102 · Answer 6 · 2026-02-24 12:39:21

102

Views

$\{f_n\}$ converges uniformly but $\lim_{n\rightarrow\infty}f_n$ doesn't exist

Published on 24 Feb 2026 - 12:39

score 150 · Answer 7 · 2026-02-24 05:36:19

150

Views

Question about the non-uniform convergence of $f(x)=2nxe^{-nx^2}$

Published on 24 Feb 2026 - 5:36

score 1.2k · Answer 8 · 2026-03-30 06:32:08

1.2k

Views

uniform convergence of a Fourier series to a continuous periodic function on $[-\pi,\pi]$

Published on 30 Mar 2026 - 6:32

score 163 · Answer 9 · 2020-04-20 17:49:38

163

Views

uniform convergence alternating series

Published on 20 Apr 2020 - 17:49

score 97 · Answer 10 · 2026-02-24 12:34:45

97

Views

Uniformly bounded and Convergence subsequence

Published on 24 Feb 2026 - 12:34

score 647 · Answer 11 · 2020-04-22 12:56:29

647

Views

Sequence of functions that converges in L∞ but not L2?

Published on 22 Apr 2020 - 12:56

score 49 · Answer 12 · 2020-04-24 13:43:36

49

Views

Uniformly convergence of $\sum_{n=0} ^{\infty} {1 \over 1+(n+x)^2}$ on $\mathbb{R}$

Published on 24 Apr 2020 - 13:43

score 80 · Answer 13 · 2020-04-24 16:14:04

80

Views

Let $F_n$ converge to $F$ uniformly on all of $\Bbb{R}$, show that $\int F_n$ need not converge to $\int F$.

Published on 24 Apr 2020 - 16:14

score 104 · Answer 14 · 2020-04-25 22:22:02

104

Views

Does $f_n$ converge uniformly on the interval $[0,0.99]$ or on the interval $[0.01,1]$

Published on 25 Apr 2020 - 22:22

score 166 · Answer 15 · 2026-03-28 15:26:02

166

Views

Convergence of an infinite product (2)

Published on 28 Mar 2026 - 15:26

List Question

Is the improper Dirichlet integral of $\sin(ax)/x$ from $0$ to infinity uniformly convergent?

Proving Continuity of power series at $x=1$

Let $B_nx=x(t-\frac{1}{n})\in L^2(\mathbb{R})$. Show that $B_n\overset{s}{\to}Id$ but $B_n\not\rightrightarrows Id$

Limits under integrals and uniform convergence.

I don't understand why we can just extend the domain of this function

$\{f_n\}$ converges uniformly but $\lim_{n\rightarrow\infty}f_n$ doesn't exist

Question about the non-uniform convergence of $f(x)=2nxe^{-nx^2}$

uniform convergence of a Fourier series to a continuous periodic function on $[-\pi,\pi]$

uniform convergence alternating series

Uniformly bounded and Convergence subsequence

Sequence of functions that converges in L∞ but not L2?

Uniformly convergence of $\sum_{n=0} ^{\infty} {1 \over 1+(n+x)^2}$ on $\mathbb{R}$

Let $F_n$ converge to $F$ uniformly on all of $\Bbb{R}$, show that $\int F_n$ need not converge to $\int F$.

Does $f_n$ converge uniformly on the interval $[0,0.99]$ or on the interval $[0.01,1]$

Convergence of an infinite product (2)

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