Question

If a trigonometric series converges to a function $f$, is the Fourier series of $f$ the original series?

score 84 · Answer 1 · 2019-09-08 07:20:29

84

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If a trigonometric series converges to a function $f$, is the Fourier series of $f$ the original series?

Published on 08 Sep 2019 - 7:20

score 566 · Answer 2 · 2019-09-14 02:57:23

566

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Arctangent sum $\sum_{n=1}^{\infty}\arctan\frac{1}{8n^{2}}$

Published on 14 Sep 2019 - 2:57

score 1.1k · Answer 3 · 2019-09-19 13:50:35

1.1k

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Fourier coefficients of a trigonometric polynomial

Published on 19 Sep 2019 - 13:50

score 161 · Answer 4 · 2019-09-21 02:43:16

161

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Proving $\sum\limits_{k=1}^{N-1}\left[\frac{\sin\left(\frac{\pi km}{N}\right)}{\sin\left(\frac{\pi k}{N}\right)}\right]^{2}=m(N-m)$

Published on 21 Sep 2019 - 2:43

score 91 · Answer 5 · 2026-03-23 01:51:10

91

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Proof of $\sum_{n=1}^\infty \frac{\cos \ n}{n}=-\frac{\ln\left(2-2 \cos(1)\right)}{2} $

Published on 23 Mar 2026 - 1:51

score 1k · Answer 6 · 2014-03-13 10:43:27

1k

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Positivness of the sum of $\frac{\sin(2k-1)x}{2k-1}$.

Published on 13 Mar 2014 - 10:43

score 258 · Answer 7 · 2014-03-18 13:31:22

258

Views

Trigonometric series problem

Published on 18 Mar 2014 - 13:31

score 102 · Answer 8 · 2014-03-29 09:22:18

102

Views

Does the expansion of $\sin x$ contradict the normal formula $\sin x = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$?

Published on 29 Mar 2014 - 9:22

score 48 · Answer 9 · 2014-04-02 04:53:02

48

Views

Series of Certain Cosines

Published on 02 Apr 2014 - 4:53

score 92 · Answer 10 · 2014-04-07 02:47:18

92

Views

Why do different trig functions sum differently?

Published on 07 Apr 2014 - 2:47

score 125 · Answer 11 · 2014-04-08 13:08:18

125

Views

Why is the Taylor expansion of $\cos$ decreasing?

Published on 08 Apr 2014 - 13:08

score 2.2k · Answer 12 · 2014-04-08 16:49:24

2.2k

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What is the Taylor series of $\frac{1}{\sin(z)}$ about $z_0 = 1$?

Published on 08 Apr 2014 - 16:49

score 182 · Answer 13 · 2014-04-13 15:46:43

182

Views

Alternating cosine series, what is the closed form?

Published on 13 Apr 2014 - 15:46

score 1.1k · Answer 14 · 2014-04-15 14:09:09

1.1k

Views

To compute $\tan1-\tan3+\tan5-\cdots+\tan89$, $\tan1+\tan3+\tan5+\cdots+\tan89$

Published on 15 Apr 2014 - 14:09

score 183 · Answer 15 · 2014-04-19 07:36:45

183

Views

What is a fast method for evaluate this trigonometric series?

Published on 19 Apr 2014 - 7:36

List Question

If a trigonometric series converges to a function $f$, is the Fourier series of $f$ the original series?

Arctangent sum $\sum_{n=1}^{\infty}\arctan\frac{1}{8n^{2}}$

Fourier coefficients of a trigonometric polynomial

Proving $\sum\limits_{k=1}^{N-1}\left[\frac{\sin\left(\frac{\pi km}{N}\right)}{\sin\left(\frac{\pi k}{N}\right)}\right]^{2}=m(N-m)$

Proof of $\sum_{n=1}^\infty \frac{\cos \ n}{n}=-\frac{\ln\left(2-2 \cos(1)\right)}{2} $

Positivness of the sum of $\frac{\sin(2k-1)x}{2k-1}$.

Trigonometric series problem

Does the expansion of $\sin x$ contradict the normal formula $\sin x = \frac{\text{Perpendicular}}{\text{Hypotenuse}}$?

Series of Certain Cosines

Why do different trig functions sum differently?

Why is the Taylor expansion of $\cos$ decreasing?

What is the Taylor series of $\frac{1}{\sin(z)}$ about $z_0 = 1$?

Alternating cosine series, what is the closed form?

To compute $\tan1-\tan3+\tan5-\cdots+\tan89$, $\tan1+\tan3+\tan5+\cdots+\tan89$

What is a fast method for evaluate this trigonometric series?

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