Question

Find $\int_0^\frac\pi2e^{i(ut+v\cos(t))}dt$ or $\int_0^\frac\pi2\sin(w+ut+v\cos(t))dt$ to invert $\frac{\sin(x)}x$

score 262 · Answer 1 · 2026-03-25 21:51:09

262

Views

Find $\int_0^\frac\pi2e^{i(ut+v\cos(t))}dt$ or $\int_0^\frac\pi2\sin(w+ut+v\cos(t))dt$ to invert $\frac{\sin(x)}x$

Published on 25 Mar 2026 - 21:51

score 41 · Answer 2 · 2026-04-01 15:40:02

41

Views

Finding elementary function that gives a given Fourier series

Published on 01 Apr 2026 - 15:40

score 115 · Answer 3 · 2023-05-31 23:03:58

115

Views

What is the span of the Fourier basis functions?

Published on 31 May 2023 - 23:03

score 35 · Answer 4 · 2026-03-27 21:36:28

35

Views

On Stein&Shakarchi's discussion on the "uniqueness of Fourier series"

Published on 27 Mar 2026 - 21:36

score 58 · Answer 5 · 2026-03-27 23:20:03

58

Views

estimates of series involving trigonometric functions

Published on 27 Mar 2026 - 23:20

score 29 · Answer 6 · 2026-03-29 12:40:43

29

Views

Given a DFT $\hat{u}$, how to approximate the Fourier coefficient $\hat{u^2}$

Published on 29 Mar 2026 - 12:40

score 66 · Answer 7 · 2023-06-05 06:14:22

66

Views

$f$ and $\hat f$ are integrable, right-hand limit and left-hand limit exist, then two limits equal.

Published on 05 Jun 2023 - 6:14

score 42 · Answer 8 · 2026-04-07 21:22:08

42

Views

The range of Fourier Transform is dense in $c_0(\mathbb Z)$

Published on 07 Apr 2026 - 21:22

score 83 · Answer 9 · 2026-04-01 07:22:40

83

Views

Difference between $L^2[0,2\pi]$ and $L^2(S^1)$

Published on 01 Apr 2026 - 7:22

score 41 · Answer 10 · 2026-04-07 21:20:45

41

Views

show that the integral is finite

Published on 07 Apr 2026 - 21:20

score 204 · Answer 11 · 2026-04-08 10:22:40

204

Views

Is there a way to approximate a function as sum of Gaussian?

Published on 08 Apr 2026 - 10:22

score 105 · Answer 12 · 2023-06-07 15:35:19

105

Views

Is an integrable function that is $\pi$-periodic and 1-periodic necessarily constant?

Published on 07 Jun 2023 - 15:35

score 166 · Answer 13 · 2023-06-07 18:16:34

166

Views

Determine the real Fourier series for $f(t) = t^2$ with $t \in [0, 1[$ which converges as quickly as possible

Published on 07 Jun 2023 - 18:16

score 27 · Answer 14 · 2023-06-08 18:24:42

27

Views

Equivalent trigonometric series solution to the Helmholtz equation

Published on 08 Jun 2023 - 18:24

score 125 · Answer 15 · 2023-06-08 20:50:29

125

Views

Fourier series of indicator function of an interval $[a,b]$ is convergent.

Published on 08 Jun 2023 - 20:50

List Question

Find $\int_0^\frac\pi2e^{i(ut+v\cos(t))}dt$ or $\int_0^\frac\pi2\sin(w+ut+v\cos(t))dt$ to invert $\frac{\sin(x)}x$

Finding elementary function that gives a given Fourier series

What is the span of the Fourier basis functions?

On Stein&Shakarchi's discussion on the "uniqueness of Fourier series"

estimates of series involving trigonometric functions

Given a DFT $\hat{u}$, how to approximate the Fourier coefficient $\hat{u^2}$

$f$ and $\hat f$ are integrable, right-hand limit and left-hand limit exist, then two limits equal.

The range of Fourier Transform is dense in $c_0(\mathbb Z)$

Difference between $L^2[0,2\pi]$ and $L^2(S^1)$

show that the integral is finite

Is there a way to approximate a function as sum of Gaussian?

Is an integrable function that is $\pi$-periodic and 1-periodic necessarily constant?

Determine the real Fourier series for $f(t) = t^2$ with $t \in [0, 1[$ which converges as quickly as possible

Equivalent trigonometric series solution to the Helmholtz equation

Fourier series of indicator function of an interval $[a,b]$ is convergent.

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