Question

Proving $f_{s}(t) = \frac{e^{-st}}{t}$ is uniformly convergent

score 51 · Answer 1 · 2018-12-29 01:02:09

51

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Proving $f_{s}(t) = \frac{e^{-st}}{t}$ is uniformly convergent

Published on 29 Dec 2018 - 1:02

score 114 · Answer 2 · 2018-12-29 12:37:01

114

Views

Proving the uniform convergence of the average sequence of $f_n(x)=\sin(nx)$

Published on 29 Dec 2018 - 12:37

score 666 · Answer 3 · 2026-03-28 16:44:18

666

Views

Uniform convergence of $ \zeta'(x) = \sum \frac{\ln(k)}{k^x}$

Published on 28 Mar 2026 - 16:44

score 194 · Answer 4 · 2018-12-30 23:07:45

194

Views

Different ways of proving that $|\sum^{\infty}_{k=1}(1-\cos(1/k))|\leq 2 $

Published on 30 Dec 2018 - 23:07

score 108 · Answer 5 · 2018-12-31 11:55:59

108

Views

Uniform convergence of power sequence

Published on 31 Dec 2018 - 11:55

score 96 · Answer 6 · 2018-12-31 17:23:50

96

Views

Prove that $ B_{n}(x)=\sum^{\infty}_{k=0} \dfrac{(-1)^k}{k!(n+k)!} \left(\dfrac{x}{2}\right)^{n+2k}$ converges uniformly.

Published on 31 Dec 2018 - 17:23

score 89 · Answer 7 · 2019-01-01 10:03:35

89

Views

Prove that $\lim\limits_{n\to\infty} \int^{b}_{a}\left(\sum^{n}_{k=1} (f_{k}(x))^{n}\right)^{1/n}dx=\int^{b}_{a}f(x) dx$

Published on 01 Jan 2019 - 10:03

score 58 · Answer 8 · 2019-01-02 20:34:10

58

Views

Uniform Cauchy and convergence clarification.

Published on 02 Jan 2019 - 20:34

score 72 · Answer 9 · 2019-01-04 03:48:03

72

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If $\int_{a}^{b} f(x) g(x) dx=0$ with $f(x)=\sum_{i=0}^{\infty} a_n x^n$, can I integrate term by term?

Published on 04 Jan 2019 - 3:48

score 27 · Answer 10 · 2026-03-25 15:42:31

27

Views

absolut and uniform convergence of complex power series on an open disk imply absolut and local uniform convergence on the whole disk of convergence

Published on 25 Mar 2026 - 15:42

score 41 · Answer 11 · 2026-02-23 12:06:38

41

Views

Uniform convergence of $\frac{y/(2N)}{\sin(y/(2N))}$ towards 1

Published on 23 Feb 2026 - 12:06

score 1.5k · Answer 12 · 2026-03-23 05:02:42

1.5k

Views

What is the main difference between pointwise and uniform convergence as defined here?

Published on 23 Mar 2026 - 5:02

score 924 · Answer 13 · 2026-02-23 12:06:22

924

Views

Uniformly convergent on each compact set of $\mathbb R$ but not on $\mathbb R$

Published on 23 Feb 2026 - 12:06

score 46 · Answer 14 · 2019-01-08 10:22:31

46

Views

Uniform convergence after transforming?

Published on 08 Jan 2019 - 10:22

score 91 · Answer 15 · 2019-01-09 01:31:02

91

Views

Uniform convergence of this series?

Published on 09 Jan 2019 - 1:31

List Question

Proving $f_{s}(t) = \frac{e^{-st}}{t}$ is uniformly convergent

Proving the uniform convergence of the average sequence of $f_n(x)=\sin(nx)$

Uniform convergence of $ \zeta'(x) = \sum \frac{\ln(k)}{k^x}$

Different ways of proving that $|\sum^{\infty}_{k=1}(1-\cos(1/k))|\leq 2 $

Uniform convergence of power sequence

Prove that $ B_{n}(x)=\sum^{\infty}_{k=0} \dfrac{(-1)^k}{k!(n+k)!} \left(\dfrac{x}{2}\right)^{n+2k}$ converges uniformly.

Prove that $\lim\limits_{n\to\infty} \int^{b}_{a}\left(\sum^{n}_{k=1} (f_{k}(x))^{n}\right)^{1/n}dx=\int^{b}_{a}f(x) dx$

Uniform Cauchy and convergence clarification.

If $\int_{a}^{b} f(x) g(x) dx=0$ with $f(x)=\sum_{i=0}^{\infty} a_n x^n$, can I integrate term by term?

absolut and uniform convergence of complex power series on an open disk imply absolut and local uniform convergence on the whole disk of convergence

Uniform convergence of $\frac{y/(2N)}{\sin(y/(2N))}$ towards 1

What is the main difference between pointwise and uniform convergence as defined here?

Uniformly convergent on each compact set of $\mathbb R$ but not on $\mathbb R$

Uniform convergence after transforming?

Uniform convergence of this series?

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