Question

What is the formula for Fourier series on the unit disk?

score 142 · Answer 1 · 2023-04-20 20:18:35

142

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What is the formula for Fourier series on the unit disk?

Published on 20 Apr 2023 - 20:18

score 62 · Answer 2 · 2026-03-28 08:36:25

62

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How do I show $\frac{1}{\sqrt L}e^{\frac{2\pi inx}{L}}$ is an orthonormal set for $L^2[a, b]$ (where $|b-a|=L$)?

Published on 28 Mar 2026 - 8:36

score 49 · Answer 3 · 2023-04-22 12:11:46

49

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Problems proving a Lemma in the Fourier Analysis of piecewise-functions

Published on 22 Apr 2023 - 12:11

score 69 · Answer 4 · 2023-04-22 17:40:11

69

Views

Fourier series approximation: does maximum of $|f(x) - S_N f(x)|$ occur when $f'$ is discontinuous?

Published on 22 Apr 2023 - 17:40

score 27 · Answer 5 · 2023-04-23 14:03:09

Why can any function be expressed as a sum of trigononmetric function? Why are fourier series equal to its function?

score 65 · Answer 6 · 2026-04-07 11:11:18

65

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Relation between logartihm and sine integral function

Published on 07 Apr 2026 - 11:11

score 207 · Answer 7 · 2026-03-31 12:54:44

207

Views

A continuous function whose Fourier series diverges at $0$?

Published on 31 Mar 2026 - 12:54

score 85 · Answer 8 · 2026-02-23 02:56:53

85

Views

Integral expression involving Bernoulli polynomial that allows to sum a trigonometric integral series.

Published on 23 Feb 2026 - 2:56

score 21 · Answer 9 · 2023-04-26 10:16:36

21

Views

Existence of a piecewise smooth, periodic, continuous function

Published on 26 Apr 2023 - 10:16

score 141 · Answer 10 · 2026-03-26 11:06:46

141

Views

Fourier series of a particular elliptic function

Published on 26 Mar 2026 - 11:06

score 19 · Answer 11 · 2023-04-27 16:18:29

19

Views

Continuity of Fourier Coefficients generalized to complex values?

Published on 27 Apr 2023 - 16:18

score 284 · Answer 12 · 2023-04-28 00:51:32

284

Views

Integral: $\int_{0}^{2\pi}\left|\sin\left(\left(n-1\right)x-\frac{\pi}{2n}\right)\cos\left(nx\right)\right|dx$

Published on 28 Apr 2023 - 0:51

score 122 · Answer 13 · 2023-04-28 07:29:51

122

Views

Why is a Fourier series expansion not always equal to the function being expanded?

Published on 28 Apr 2023 - 7:29

score 101 · Answer 14 · 2023-04-28 13:48:21

101

Views

$C^{\infty}$ solutions to the functional equation $f(2x)=2\sin(x)f'(x)$

Published on 28 Apr 2023 - 13:48

score 112 · Answer 15 · 2023-04-28 16:21:58

112

Views

Checking Fourier coefficients

Published on 28 Apr 2023 - 16:21

List Question

What is the formula for Fourier series on the unit disk?

How do I show $\frac{1}{\sqrt L}e^{\frac{2\pi inx}{L}}$ is an orthonormal set for $L^2[a, b]$ (where $|b-a|=L$)?

Problems proving a Lemma in the Fourier Analysis of piecewise-functions

Fourier series approximation: does maximum of $|f(x) - S_N f(x)|$ occur when $f'$ is discontinuous?

Why can any function be expressed as a sum of trigononmetric function? Why are fourier series equal to its function?

Relation between logartihm and sine integral function

A continuous function whose Fourier series diverges at $0$?

Integral expression involving Bernoulli polynomial that allows to sum a trigonometric integral series.

Existence of a piecewise smooth, periodic, continuous function

Fourier series of a particular elliptic function

Continuity of Fourier Coefficients generalized to complex values?

Integral: $\int_{0}^{2\pi}\left|\sin\left(\left(n-1\right)x-\frac{\pi}{2n}\right)\cos\left(nx\right)\right|dx$

Why is a Fourier series expansion not always equal to the function being expanded?

$C^{\infty}$ solutions to the functional equation $f(2x)=2\sin(x)f'(x)$

Checking Fourier coefficients

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