Question

Why is the infinite sum of this trigonometric series =zero yet when I evaluate the finite sum and take the limit $n \to \infty$ it not well defined?

score 70 · Answer 1 · 2024-03-06 23:38:06

Why is the infinite sum of this trigonometric series =zero yet when I evaluate the finite sum and take the limit $n \to \infty$ it not well defined?

score 48 · Answer 2 · 2024-03-10 09:37:40

48

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prove that $\sum_{n = 1}^{\infty} \frac{|\sin(nx)|}{n}$ is divergent

Published on 10 Mar 2024 - 9:37

score 77 · Answer 3 · 2024-03-17 06:18:27

77

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Is it true that $\min\{x, y\} = 2 \sum_{n \geq 1, n~\text{odd}} \frac{\sin(n x) \sin(ny)}{n^2}$?

Published on 17 Mar 2024 - 6:18

score 64 · Answer 4 · 2024-03-20 19:51:58

64

Views

Behavior of an Infinite Series

Published on 20 Mar 2024 - 19:51

score 198 · Answer 5 · 2024-03-21 18:11:15

198

Views

Behavior of function $\sum_{j = n}^\infty \frac{\sin^2((2j-1) \pi x)}{(2j-1)^2}$

Published on 21 Mar 2024 - 18:11

score 48 · Answer 6 · 2015-01-05 21:38:00

48

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A trigonometric series with differences of cosines of cube roots

Published on 05 Jan 2015 - 21:38

score 339 · Answer 7 · 2015-01-07 06:54:38

339

Views

Is there any identity for $\sum_{k=0}^{n-1}\tan(x+ka) $??

Published on 07 Jan 2015 - 6:54

score 411 · Answer 8 · 2015-01-09 19:19:52

411

Views

Number of iterations to reach cosine's fixed point

Published on 09 Jan 2015 - 19:19

score 70 · Answer 9 · 2015-01-21 21:35:49

70

Views

Fourier series question - represent $x$ as a series of $\cos$

Published on 21 Jan 2015 - 21:35

score 1.9k · Answer 10 · 2015-01-26 21:43:16

1.9k

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Determine the limit of a series, involving trigonometric functions: $\sum \frac{\sin(nx)}{n^3}$ and $\frac{\cos(nx)}{n^2}$

Published on 26 Jan 2015 - 21:43

score 67 · Answer 11 · 2015-02-01 02:18:00

67

Views

Integral $\int_0^{\infty}\cos(a_0+a_1x+a_2x^2)\frac{1}{x^2+\frac{1}{4}}dx$

Published on 01 Feb 2015 - 2:18

score 6.5k · Answer 12 · 2015-02-04 06:28:42

6.5k

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Deducing a $\cos (kx)$ summation from the $e^{ikx}$ summation

Published on 04 Feb 2015 - 6:28

score 561 · Answer 13 · 2015-02-04 17:08:52

561

Views

Evaluating $(1+\cos\frac{\pi}{8})(1+\cos\frac{3\pi}{8}) (1+\cos\frac{5\pi}{8})(1+\cos\frac{7\pi}{8})$

Published on 04 Feb 2015 - 17:08

score 50 · Answer 14 · 2026-03-25 23:08:02

50

Views

Trigonometical sum from Fourier analysis

Published on 25 Mar 2026 - 23:08

score 70 · Answer 15 · 2015-02-20 10:26:59

70

Views

General form of $\sum_{i=1}^{k} \frac{1}{k}\tan(\frac{i\theta}{k})$

Published on 20 Feb 2015 - 10:26

List Question

Why is the infinite sum of this trigonometric series =zero yet when I evaluate the finite sum and take the limit $n \to \infty$ it not well defined?

prove that $\sum_{n = 1}^{\infty} \frac{|\sin(nx)|}{n}$ is divergent

Is it true that $\min\{x, y\} = 2 \sum_{n \geq 1, n~\text{odd}} \frac{\sin(n x) \sin(ny)}{n^2}$?

Behavior of an Infinite Series

Behavior of function $\sum_{j = n}^\infty \frac{\sin^2((2j-1) \pi x)}{(2j-1)^2}$

A trigonometric series with differences of cosines of cube roots

Is there any identity for $\sum_{k=0}^{n-1}\tan(x+ka) $??

Number of iterations to reach cosine's fixed point

Fourier series question - represent $x$ as a series of $\cos$

Determine the limit of a series, involving trigonometric functions: $\sum \frac{\sin(nx)}{n^3}$ and $\frac{\cos(nx)}{n^2}$

Integral $\int_0^{\infty}\cos(a_0+a_1x+a_2x^2)\frac{1}{x^2+\frac{1}{4}}dx$

Deducing a $\cos (kx)$ summation from the $e^{ikx}$ summation

Evaluating $(1+\cos\frac{\pi}{8})(1+\cos\frac{3\pi}{8}) (1+\cos\frac{5\pi}{8})(1+\cos\frac{7\pi}{8})$

Trigonometical sum from Fourier analysis

General form of $\sum_{i=1}^{k} \frac{1}{k}\tan(\frac{i\theta}{k})$

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