List questions from fourier-series

Published on 09 Apr 2026 - 11:51

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Fourier Series Notation

Published on 10 Apr 2026 - 3:31

103

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Finding the coefficients in fourier series and parseval's formula for $e^{x} = \sum_{n=-\infty}^{\infty}c_n e_n(x)$

Published on 14 Apr 2026 - 6:43

618

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Orthonormal set of basis functions in $L^2([a,b])$

Published on 14 Apr 2026 - 21:30

652

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Fourier series coefficients' relation to original function

Published on 11 Apr 2026 - 5:32

215

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If $\int_0^{2\pi} q = 0$, then $\lim_{n \to \infty} \int_0^{2\pi}p(x)q(nx) \, dx= 0$

Published on 17 Apr 2026 - 10:54

108

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Fourier series for $\min \{0, \cos x\}$

Published on 14 Apr 2026 - 20:23

179

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$\sum\left|\sin\alpha n+\sin\beta n\right|/n=\infty$ when $\alpha\neq-\beta$

Published on 20 Apr 2026 - 12:00

106

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Problem: If $f\in L^1[0,1]$, show that $\lim_{n\to\infty}\frac{1}{n}\sum_{k=0}^{n-1}f(x+\frac{k}{n})=\int_0^1 f(s)ds$ in $L^1[0,1]$.

Published on 15 Apr 2026 - 23:15

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Deriving formula from Fourier series: $\frac{\pi^2}{12} = \sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^2}$

Published on 13 Apr 2026 - 17:52

413

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Convergence of Fourier series in $L^2$ space

Published on 14 Apr 2026 - 2:48

58

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Is my formula for DFT correct?

Published on 11 Apr 2026 - 6:27

62

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Fourier coefficients of $\;\log\log$

Published on 26 Mar 2026 - 10:46

2k

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How does the orthogonality of sine and cosine figure in the Fourier series?

Published on 10 Apr 2026 - 9:37

58

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Complex series should sum to zero but it's a puzzle

Published on 09 Apr 2026 - 4:27

List Question

A BBP-type series

Fourier Series Notation

Finding the coefficients in fourier series and parseval's formula for $e^{x} = \sum_{n=-\infty}^{\infty}c_n e_n(x)$

Orthonormal set of basis functions in $L^2([a,b])$

Fourier series coefficients' relation to original function

If $\int_0^{2\pi} q = 0$, then $\lim_{n \to \infty} \int_0^{2\pi}p(x)q(nx) \, dx= 0$

Fourier series for $\min \{0, \cos x\}$

$\sum\left|\sin\alpha n+\sin\beta n\right|/n=\infty$ when $\alpha\neq-\beta$

Problem: If $f\in L^1[0,1]$, show that $\lim_{n\to\infty}\frac{1}{n}\sum_{k=0}^{n-1}f(x+\frac{k}{n})=\int_0^1 f(s)ds$ in $L^1[0,1]$.

Deriving formula from Fourier series: $\frac{\pi^2}{12} = \sum\limits_{n=1}^{\infty} \frac{(-1)^{n+1}}{n^2}$

Convergence of Fourier series in $L^2$ space

Is my formula for DFT correct?

Fourier coefficients of $\;\log\log$

How does the orthogonality of sine and cosine figure in the Fourier series?

Complex series should sum to zero but it's a puzzle

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