Question

Use Fourier series to show $\cos(x)=\frac{8}{\pi}\sum_{n=1}^{\infty}\frac{n \sin(2n x)}{4n^2-1}$ on $(0,\pi)$

score 84 · Answer 1 · 2020-03-28 02:37:30

84

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Use Fourier series to show $\cos(x)=\frac{8}{\pi}\sum_{n=1}^{\infty}\frac{n \sin(2n x)}{4n^2-1}$ on $(0,\pi)$

Published on 28 Mar 2020 - 2:37

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517

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483

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64

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List Question

Use Fourier series to show $\cos(x)=\frac{8}{\pi}\sum_{n=1}^{\infty}\frac{n \sin(2n x)}{4n^2-1}$ on $(0,\pi)$

Exercise 11 Chapter 3 From Stein's Fourier Analysis

Does the Fourier inversion theorem hold if $f$ is square-integrable?

Is there a method for parallel frequency sources sum where individual sources do not contain the total sum mode?

Inverse Fourier Transform of $(\frac{\sin(k)}{k})^t$ when $t$ is not an integer

A question on the product of positive definite functions

understanding the proof: there exists a trigonometric polynomial, which an $(\epsilon, \delta)$ approximation to the identity

Fourier transform of $K(x)=\log \left|\frac{1+x}{x}\right|$

Doubt on the convergence of this series (looks like a very hard and interesting issue).

How to get the DC bias in the Fourier transform of the square wave?

Why is the fft not implemented monotonically?

Solution to the Massive Laplacian Operator

Problem of determining if sinusoidal function has real zeros in closed form

A question on zygmund class estimates

Solving an ODE via Fourier transforms - solution not integrable

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