List questions from trigonometric-series

Published on 25 Jul 2016 - 21:43

129

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How can I prove this ? $\sum\limits_{i=1}^N \frac{1}{\sin^2(\frac{i \pi}{2 N})} = \frac{1}{3}(2N^2+1)$

Published on 29 Jul 2016 - 7:52

515

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A Maclaurin expansion of $\arccos(-z)$ using only non-negative coefficients

Published on 01 Aug 2016 - 20:05

182

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Looking for a proof of the (general) Salem-Zygmund theorem

Published on 26 Mar 2026 - 14:22

100

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A variant of Hilbert's inequality

Published on 02 Aug 2016 - 21:39

151

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How to compute $\sum_{k=1}^n \frac{1}{\sin^2(\frac{k\pi}{2n+1})}$ efficiently?

Published on 04 Aug 2016 - 17:18

89

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Bernstein sets are sets of uniqueness

Published on 26 Mar 2026 - 14:19

2.7k

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Fourier Series for $f(x)=x, 0<x<\pi$

Published on 07 Aug 2016 - 4:19

261

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What is the value of $\sin^2(6°)- \sin^2(12°)+ \sin^2(18)-\cdots \text{till $15$th term}$?

Published on 16 Aug 2016 - 8:39

5.8k

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Fourier Series Real life application

Published on 20 Aug 2016 - 2:17

60

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solution of a trigonometric identity

Published on 20 Aug 2016 - 5:32

137

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Taylor Expansion of a Trig Function

Published on 23 Aug 2016 - 12:19

204

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On calculations from $\zeta(3)=\frac{2}{\pi}\sum_{n=1}^\infty\int_0^\infty \frac{\sin ((n+1)x)\sin (nx)}{(xn^2)^2}dx$

Published on 24 Aug 2016 - 17:32

514

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Can this "formal proof" of irrationality of $\pi$ be made rigorous?

Published on 31 Aug 2016 - 19:34

86

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Finding the value of an infinite trigonometric series

Published on 01 Sep 2016 - 7:39

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maximising sinusoidal functions

How can I prove this ? $\sum\limits_{i=1}^N \frac{1}{\sin^2(\frac{i \pi}{2 N})} = \frac{1}{3}(2N^2+1)$

A Maclaurin expansion of $\arccos(-z)$ using only non-negative coefficients

Looking for a proof of the (general) Salem-Zygmund theorem

A variant of Hilbert's inequality

How to compute $\sum_{k=1}^n \frac{1}{\sin^2(\frac{k\pi}{2n+1})}$ efficiently?

Bernstein sets are sets of uniqueness

Fourier Series for $f(x)=x, 0<x<\pi$

What is the value of $\sin^2(6°)- \sin^2(12°)+ \sin^2(18)-\cdots \text{till $15$th term}$?

Fourier Series Real life application

solution of a trigonometric identity

Taylor Expansion of a Trig Function

On calculations from $\zeta(3)=\frac{2}{\pi}\sum_{n=1}^\infty\int_0^\infty \frac{\sin ((n+1)x)\sin (nx)}{(xn^2)^2}dx$

Can this "formal proof" of irrationality of $\pi$ be made rigorous?

Finding the value of an infinite trigonometric series

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