List questions from fourier-series

Published on 09 Apr 2026 - 14:33

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Fourier series with initial conditions

Published on 11 Apr 2026 - 15:45

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Parseval's theorem rewritten in Fourier series

Published on 09 Apr 2026 - 11:59

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Fourier series proving $\sum \frac{1}{n^4} = \frac{\pi^4}{90}$

Published on 12 Apr 2026 - 12:04

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From $\frac{1}{2}+\sum_{n=1}^\infty \frac{4}{\pi^2 n^2}\cos(2\pi nx)=(1-2x)^2$ to $\sum_{n=1}^\infty \frac{1}{n^4}=\frac{\pi^4}{90}$

Published on 14 Apr 2026 - 22:54

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Calculating Fourier expansion without using $\frac{a_o}{2}+\sum_{n=1}^{\infty} (a_n\cos(\frac{2n\pi}{T})t+b_n\sin(\frac{2n\pi}{T})t$

Published on 16 Apr 2026 - 1:25

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Fourier series of a piecewise continuous (constant) function. Is my solution correct?

Published on 12 Apr 2026 - 15:18

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Finding Fourier Coefficients given $f(x) = \left\{ \begin{array}{rcl} -4\,x & \text{if} & -\pi<x<0 \\ 4\,x & \text{if} & 0<x<\pi \end{array}\right.$

Published on 16 Apr 2026 - 11:05

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Use separation of variables to solve BVP with mixed boundary conditions.

Published on 14 Apr 2026 - 9:30

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Lemma 1.4.3 A First Course in Harmonic Analysis

Published on 14 Apr 2026 - 0:44

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simplifying an expression of the complex exponential

Published on 12 Apr 2026 - 12:56

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Derive Factor in Fourier Series

Published on 10 Apr 2026 - 1:21

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Limit is $0$ uniformly for fourier coefficients

Published on 14 Apr 2026 - 21:06

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Theorem 2.3.2 A First Course in Harmonic Analysis

Published on 14 Apr 2026 - 13:33

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calculating sum of a series using fourier series

Published on 11 Apr 2026 - 0:32

List Question

Fourier Theorem

Fourier series with initial conditions

Parseval's theorem rewritten in Fourier series

Fourier series proving $\sum \frac{1}{n^4} = \frac{\pi^4}{90}$

From $\frac{1}{2}+\sum_{n=1}^\infty \frac{4}{\pi^2 n^2}\cos(2\pi nx)=(1-2x)^2$ to $\sum_{n=1}^\infty \frac{1}{n^4}=\frac{\pi^4}{90}$

Calculating Fourier expansion without using $\frac{a_o}{2}+\sum_{n=1}^{\infty} (a_n\cos(\frac{2n\pi}{T})t+b_n\sin(\frac{2n\pi}{T})t$

Fourier series of a piecewise continuous (constant) function. Is my solution correct?

Finding Fourier Coefficients given $f(x) = \left\{ \begin{array}{rcl} -4\,x & \text{if} & -\pi<x<0 \\ 4\,x & \text{if} & 0<x<\pi \end{array}\right.$

Use separation of variables to solve BVP with mixed boundary conditions.

Lemma 1.4.3 A First Course in Harmonic Analysis

simplifying an expression of the complex exponential

Derive Factor in Fourier Series

Limit is $0$ uniformly for fourier coefficients

Theorem 2.3.2 A First Course in Harmonic Analysis

calculating sum of a series using fourier series

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