Question

Showing the Series $\sum_{n=1}^{\infty}c_{n}$ convergences and that it's abel summable to s?

score 289 · Answer 1 · 2017-05-19 17:18:55

289

Views

Showing the Series $\sum_{n=1}^{\infty}c_{n}$ convergences and that it's abel summable to s?

Published on 19 May 2017 - 17:18

score 1.1k · Answer 2 · 2017-06-18 15:36:20

1.1k

Views

Proving $\sin(x) + \sin(2x) + \sin(3x)+ \cdots +\sin(nx) = \frac{cos(1/2) - cos(n-1/2)}{2 \sin(1/2)2}$ via Ceasro Summation?

Published on 18 Jun 2017 - 15:36

score 634 · Answer 3 · 2017-07-11 12:32:15

634

Views

Showing Abel Means of a Fourier Series Converge Uniformaly to $f$?

Published on 11 Jul 2017 - 12:32

score 736 · Answer 4 · 2017-07-11 22:25:28

Verifying $|F(r)| \geq \frac{1}{1-r}\log(\frac{1}{1-r}) $ and $|F(re^{i \theta})| \geq c_{q/r}\frac{1}{1-r}\log({\log(\frac{1}{1-r})})$

score 207 · Answer 5 · 2017-08-16 12:19:25

207

Views

A couple of difficulties in Tauber theory lecture notes of prof. Yum-Tong Siu

Published on 16 Aug 2017 - 12:19

score 39 · Answer 6 · 2020-12-03 17:35:51

39

Views

Asymptotics of convolution of a series given the asymptotics of the series

Published on 03 Dec 2020 - 17:35

score 69 · Answer 7 · 2021-02-16 11:46:34

69

Views

From averages with weight $1/x \log e x$ to averages with weight $1/x$

Published on 16 Feb 2021 - 11:46

score 93 · Answer 8 · 2021-02-22 16:57:09

93

Views

Asymptotic expansion at $x=1^-$ for $\sum_{n=1}^{\infty} x^{a_n}$

Published on 22 Feb 2021 - 16:57

score 84 · Answer 9 · 2021-03-03 01:17:56

84

Views

Limiting behavior of a function defined by a Lambert-type series

Published on 03 Mar 2021 - 1:17

score 183 · Answer 10 · 2021-11-05 10:54:28

183

Views

How to prove this Tauberian theorem

Published on 05 Nov 2021 - 10:54

score 38 · Answer 11 · 2021-11-22 22:13:44

38

Views

Convergence speed of the tail of distribution using Tauberian remainder theorem

Published on 22 Nov 2021 - 22:13

score 750 · Answer 12 · 2022-03-19 04:10:53

750

Views

Find the limit $\lim\limits_{s\to0^+}\sum_{n=1}^\infty\frac{\sin n}{n^s}$

Published on 19 Mar 2022 - 4:10

score 147 · Answer 13 · 2022-07-09 16:19:20

147

Views

Hardy–Littlewood Tauberian theorem for Laplace transform

Published on 09 Jul 2022 - 16:19

score 73 · Answer 14 · 2022-08-18 17:25:47

73

Views

Asymptotics of moment generating function

Published on 18 Aug 2022 - 17:25

score 43 · Answer 15 · 2022-10-22 05:49:44

43

Views

Negativity of an analytic function on $[0,1)$

Published on 22 Oct 2022 - 5:49

List Question

Showing the Series $\sum_{n=1}^{\infty}c_{n}$ convergences and that it's abel summable to s?

Proving $\sin(x) + \sin(2x) + \sin(3x)+ \cdots +\sin(nx) = \frac{cos(1/2) - cos(n-1/2)}{2 \sin(1/2)2}$ via Ceasro Summation?

Showing Abel Means of a Fourier Series Converge Uniformaly to $f$?

Verifying $|F(r)| \geq \frac{1}{1-r}\log(\frac{1}{1-r}) $ and $|F(re^{i \theta})| \geq c_{q/r}\frac{1}{1-r}\log({\log(\frac{1}{1-r})})$

A couple of difficulties in Tauber theory lecture notes of prof. Yum-Tong Siu

Asymptotics of convolution of a series given the asymptotics of the series

From averages with weight $1/x \log e x$ to averages with weight $1/x$

Asymptotic expansion at $x=1^-$ for $\sum_{n=1}^{\infty} x^{a_n}$

Limiting behavior of a function defined by a Lambert-type series

How to prove this Tauberian theorem

Convergence speed of the tail of distribution using Tauberian remainder theorem

Find the limit $\lim\limits_{s\to0^+}\sum_{n=1}^\infty\frac{\sin n}{n^s}$

Hardy–Littlewood Tauberian theorem for Laplace transform

Asymptotics of moment generating function

Negativity of an analytic function on $[0,1)$

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