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Conditions for a finite Fourier series

score 689 · Answer 1 · 2026-04-12 16:13:12

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Conditions for a finite Fourier series

Published on 12 Apr 2026 - 16:13

score 959 · Answer 2 · 2026-04-16 01:07:05

959

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$f,g$ are two continuous functions with period$=1$, are the Fourier coefficients $f*g=f(n)g(n)$?

Published on 16 Apr 2026 - 1:07

score 312 · Answer 3 · 2026-04-14 14:15:00

312

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How to prove $(1-2x)^2=1/3+4/\pi^2\sum_1^\infty \cos(2n x \pi)/n^2$ for $x \in [0,1)$?

Published on 14 Apr 2026 - 14:15

score 2.8k · Answer 4 · 2026-04-15 04:33:47

2.8k

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Prove: Fourier series of $e^{\cos x} \sin (\sin x)$ is $\sum_{n=0}^{\infty}\frac{\sin (nx)}{n!}$

Published on 15 Apr 2026 - 4:33

score 1.3k · Answer 5 · 2026-04-11 12:02:22

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Analytic functions and Fourier Series

Published on 11 Apr 2026 - 12:02

score 154 · Answer 6 · 2026-04-15 15:23:59

154

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Proving the locus of a Fourier series is a system of perpendicular lines

Published on 15 Apr 2026 - 15:23

score 1k · Answer 7 · 2026-04-15 13:14:18

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When convergence in mean implies uniform convergence?

Published on 15 Apr 2026 - 13:14

score 9.7k · Answer 8 · 2026-04-15 08:51:08

9.7k

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Uniform convergence of Fourier Series

Published on 15 Apr 2026 - 8:51

score 6.6k · Answer 9 · 2026-04-12 19:09:27

6.6k

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Performing a differentiation on a Fourier series

Published on 12 Apr 2026 - 19:09

score 11.9k · Answer 10 · 2026-04-12 07:10:47

11.9k

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Scaling property of Fourier series and Fourier Transform

Published on 12 Apr 2026 - 7:10

score 501 · Answer 11 · 2026-04-16 00:00:57

501

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Heuristic\iterated construction of the Weierstrass nowhere differentiable function.

Published on 16 Apr 2026 - 0:00

score 238 · Answer 12 · 2026-04-10 22:19:16

238

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How do I calculate Fourier series of an $f(x)$ with discontinuities inside its period?

Published on 10 Apr 2026 - 22:19

score 5.5k · Answer 13 · 2026-04-16 21:10:23

5.5k

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$S(x)=\sum_{n=1}^{\infty}a_n \sin(nx) $, $a_n$ is monotonic decreasing $a_n\to 0$: Show uniformly converges within $[\epsilon, 2\pi - \epsilon]$

Published on 16 Apr 2026 - 21:10

score 32.7k · Answer 14 · 2026-04-13 23:22:34

32.7k

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Use Fourier series for computing $\sum_{n=1}^{\infty}\frac{1}{(2n-1)^2}$

Published on 13 Apr 2026 - 23:22

score 1.6k · Answer 15 · 2026-04-10 16:33:19

1.6k

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Fourier transforms of cos and sin

Published on 10 Apr 2026 - 16:33

List Question

Conditions for a finite Fourier series

$f,g$ are two continuous functions with period$=1$, are the Fourier coefficients $f*g=f(n)g(n)$?

How to prove $(1-2x)^2=1/3+4/\pi^2\sum_1^\infty \cos(2n x \pi)/n^2$ for $x \in [0,1)$?

Prove: Fourier series of $e^{\cos x} \sin (\sin x)$ is $\sum_{n=0}^{\infty}\frac{\sin (nx)}{n!}$

Analytic functions and Fourier Series

Proving the locus of a Fourier series is a system of perpendicular lines

When convergence in mean implies uniform convergence?

Uniform convergence of Fourier Series

Performing a differentiation on a Fourier series

Scaling property of Fourier series and Fourier Transform

Heuristic\iterated construction of the Weierstrass nowhere differentiable function.

How do I calculate Fourier series of an $f(x)$ with discontinuities inside its period?

$S(x)=\sum_{n=1}^{\infty}a_n \sin(nx) $, $a_n$ is monotonic decreasing $a_n\to 0$: Show uniformly converges within $[\epsilon, 2\pi - \epsilon]$

Use Fourier series for computing $\sum_{n=1}^{\infty}\frac{1}{(2n-1)^2}$

Fourier transforms of cos and sin

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