List questions from trigonometric-series

Published on 09 Dec 2016 - 18:07

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Is there an alternative form/identity for $\prod_{k=1}^{m} \cos(2^kx)$?

Published on 20 Dec 2016 - 18:58

57

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$\sum_{n \neq 0} {\dfrac{\sin(n\vartheta)}{n}}$ does not converge absolutely, when $0 < \vartheta < \pi$.

Published on 26 Mar 2026 - 17:34

245

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$\dfrac{2}{\pi} = \dfrac{\sqrt 2}{2} \cdot \dfrac{\sqrt {2+\sqrt 2}}{2} \cdot\dfrac{\sqrt {2+\sqrt {2+\sqrt 2}}}{2} \cdots $

Published on 21 Dec 2016 - 10:14

571

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Trigonometric system is complete proof-Lebesgue Integration by parts

Published on 21 Dec 2016 - 15:36

111

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Series representation of $|\cos\theta|^{1/2}+|\sin\theta|^{1/2}$

Published on 23 Dec 2016 - 1:31

302

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Basel problem, but with cosines

Published on 23 Dec 2016 - 15:23

363

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Finding the partial sums of an infinite series

Published on 24 Dec 2016 - 0:02

174

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Functions with the property $\frac{d}{dx}(f(x)\cdot f(x))=f(2x)$

Published on 25 Dec 2016 - 16:07

1.7k

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Power Series involving Double Factorials

Published on 29 Dec 2016 - 21:54

224

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Cosine Series Converging in Sense of Distributions

Published on 03 Jan 2017 - 17:46

144

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How to derive the equation from trigonometric funtions

Published on 05 Jan 2017 - 6:38

87

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Insight about $\sum_{n=1}^\infty \sum_{m=1}^\infty 2e^{\frac{-\pi}{2} \sqrt{m^2+n^2}}\cos(my) \cos(nx)$

Published on 05 Jan 2017 - 22:23

195

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Trigonometric sum of tangents series

Published on 06 Jan 2017 - 8:16

553

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Expanding $\frac{(\text{cis}\ 75^\circ-\text{cis}\ 155^\circ)(1-\cos 8^\circ+i \sin 8 ^\circ)}{2-2\cos 8^\circ}$

Published on 14 Jan 2017 - 20:48

List Question

find $\sum_{k=1}^{13}\sin^{2n}\left({\frac{k\pi}{13}}\right)$?

Is there an alternative form/identity for $\prod_{k=1}^{m} \cos(2^kx)$?

$\sum_{n \neq 0} {\dfrac{\sin(n\vartheta)}{n}}$ does not converge absolutely, when $0 < \vartheta < \pi$.

$\dfrac{2}{\pi} = \dfrac{\sqrt 2}{2} \cdot \dfrac{\sqrt {2+\sqrt 2}}{2} \cdot\dfrac{\sqrt {2+\sqrt {2+\sqrt 2}}}{2} \cdots $

Trigonometric system is complete proof-Lebesgue Integration by parts

Series representation of $|\cos\theta|^{1/2}+|\sin\theta|^{1/2}$

Basel problem, but with cosines

Finding the partial sums of an infinite series

Functions with the property $\frac{d}{dx}(f(x)\cdot f(x))=f(2x)$

Power Series involving Double Factorials

Cosine Series Converging in Sense of Distributions

How to derive the equation from trigonometric funtions

Insight about $\sum_{n=1}^\infty \sum_{m=1}^\infty 2e^{\frac{-\pi}{2} \sqrt{m^2+n^2}}\cos(my) \cos(nx)$

Trigonometric sum of tangents series

Expanding $\frac{(\text{cis}\ 75^\circ-\text{cis}\ 155^\circ)(1-\cos 8^\circ+i \sin 8 ^\circ)}{2-2\cos 8^\circ}$

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