Question

Sum of uniformly convergent sequences converges to sum of limit functions

score 3.6k · Answer 1 · 2018-04-05 19:45:07

3.6k

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Sum of uniformly convergent sequences converges to sum of limit functions

Published on 05 Apr 2018 - 19:45

score 42 · Answer 2 · 2018-04-06 10:06:44

42

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$S_N(x)=\sum_{k=-N}^N\frac{1}{x-k}, x \in \mathbb{R} \setminus \mathbb{Z}$ converges absolutely on every compact subset $[a,b] $ against $h(x)$

Published on 06 Apr 2018 - 10:06

score 685 · Answer 3 · 2026-03-25 02:03:05

685

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Sequence of bijective $C^1$ mappings uniformly convergent to non-bijective limit function

Published on 25 Mar 2026 - 2:03

score 852 · Answer 4 · 2018-04-07 21:26:27

852

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Can $f_n$ bounded uniformly converge to $f$ unbounded?

Published on 07 Apr 2018 - 21:26

score 265 · Answer 5 · 2026-02-22 23:39:08

265

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Understanding technique for proving uniform convergence of sequence of functions

Published on 22 Feb 2026 - 23:39

score 468 · Answer 6 · 2018-04-10 18:51:37

468

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difficulty to deal with $\min(n,\frac{1}{x})$ in a problem that asks to prove $\{f_n\}_n$ is not uniformly convergent.

Published on 10 Apr 2018 - 18:51

score 87 · Answer 7 · 2018-04-11 00:46:54

87

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Let $B_n:=\sum_{k=0}^n f(k/n)B_{n,k}$. Show that $\lim_{n\to\infty}B_n(f)=f$

Published on 11 Apr 2018 - 0:46

score 189 · Answer 8 · 2026-02-22 23:40:37

189

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Convergence of sequence of functions $\sum_{n\ge1 }ne^{-nx^2}$

Published on 22 Feb 2026 - 23:40

score 61 · Answer 9 · 2018-04-12 17:23:47

61

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Uniform convergence of the function series $\sum_{n\geq 0}\frac{\sin{x}}{1+n^2 x^2}$

Published on 12 Apr 2018 - 17:23

score 50 · Answer 10 · 2026-03-26 23:09:48

50

Views

Finding interval of uniform convergence for $\sin^2(tx)/x^2$

Published on 26 Mar 2026 - 23:09

score 45 · Answer 11 · 2018-04-13 01:19:14

45

Views

Real Analysis: Showing uniform convergence on $[, \infty)$ and $[0,\infty)$ for sequence of functions

Published on 13 Apr 2018 - 1:19

score 71 · Answer 12 · 2018-04-13 10:48:54

71

Views

Show series of functions is uniformly convergent on $[a,\infty)$ for $a>0$.

Published on 13 Apr 2018 - 10:48

score 103 · Answer 13 · 2026-03-26 04:52:01

103

Views

Sequence of functions converges normally to $e^z$

Published on 26 Mar 2026 - 4:52

score 1.2k · Answer 14 · 2018-04-14 11:36:18

1.2k

Views

Does the series of functions, with $ f_n(x) = (-1)^n x^n (1-x)$ converge uniformly on $[0,1]$

Published on 14 Apr 2018 - 11:36

score 138 · Answer 15 · 2026-03-26 12:36:34

138

Views

Compact convergence of a series of functions

Published on 26 Mar 2026 - 12:36

List Question

Sum of uniformly convergent sequences converges to sum of limit functions

$S_N(x)=\sum_{k=-N}^N\frac{1}{x-k}, x \in \mathbb{R} \setminus \mathbb{Z}$ converges absolutely on every compact subset $[a,b] $ against $h(x)$

Sequence of bijective $C^1$ mappings uniformly convergent to non-bijective limit function

Can $f_n$ bounded uniformly converge to $f$ unbounded?

Understanding technique for proving uniform convergence of sequence of functions

difficulty to deal with $\min(n,\frac{1}{x})$ in a problem that asks to prove $\{f_n\}_n$ is not uniformly convergent.

Let $B_n:=\sum_{k=0}^n f(k/n)B_{n,k}$. Show that $\lim_{n\to\infty}B_n(f)=f$

Convergence of sequence of functions $\sum_{n\ge1 }ne^{-nx^2}$

Uniform convergence of the function series $\sum_{n\geq 0}\frac{\sin{x}}{1+n^2 x^2}$

Finding interval of uniform convergence for $\sin^2(tx)/x^2$

Real Analysis: Showing uniform convergence on $[, \infty)$ and $[0,\infty)$ for sequence of functions

Show series of functions is uniformly convergent on $[a,\infty)$ for $a>0$.

Sequence of functions converges normally to $e^z$

Does the series of functions, with $ f_n(x) = (-1)^n x^n (1-x)$ converge uniformly on $[0,1]$

Compact convergence of a series of functions

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