Question

A problem arises when computing the integral of the sinc function using the Fourier transform.

score 317 · Answer 1 · 2026-04-11 05:16:31

317

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A problem arises when computing the integral of the sinc function using the Fourier transform.

Published on 11 Apr 2026 - 5:16

score 104 · Answer 2 · 2026-04-16 20:56:57

104

Views

$f_n(t)=\int_{-n}^{n} \frac{\sin x}{x}\cdot e^{-itx}\ dx$ converges uniformly near $t=0$.

Published on 16 Apr 2026 - 20:56

score 285 · Answer 3 · 2026-04-11 20:11:33

285

Views

Please Help: Derivative of a sinc function.

Published on 11 Apr 2026 - 20:11

score 210 · Answer 4 · 2026-03-25 23:22:27

210

Views

Fourier transform of $ \frac{e^{-|\xi|^2 |t|}}{|\xi|^2} $

Published on 25 Mar 2026 - 23:22

score 1.1k · Answer 5 · 2026-04-12 18:03:17

1.1k

Views

Computing the Fourier transform of exponential decay in $\mathbb{R}^2$

Published on 12 Apr 2026 - 18:03

score 119 · Answer 6 · 2026-04-16 15:15:41

119

Views

Fourier transform of $\exp{\left(irx/\sqrt{1-ix}\right)}/(1-ix)$.

Published on 16 Apr 2026 - 15:15

score 147 · Answer 7 · 2026-04-13 04:26:15

147

Views

Fourier Transform of $\frac{1}{|x|^2-1}$ in $\mathbb{R}^3$

Published on 13 Apr 2026 - 4:26

score 101 · Answer 8 · 2026-04-13 15:15:08

101

Views

Computing Fibonacci numbers with generating function

Published on 13 Apr 2026 - 15:15

score 30 · Answer 9 · 2026-04-14 22:16:33

30

Views

A non-trivial condition on $f$ such that $F: \mathbb{R}^2\to\mathbb{C}: F(x,t)=\int_{\mathbb{R}}f(x,y)e^{-2\pi iyt}dy$ is a continuous function.

Published on 14 Apr 2026 - 22:16

score 83 · Answer 10 · 2026-04-10 16:04:16

83

Views

2D spatial Fourier transform integral calculation

Published on 10 Apr 2026 - 16:04

score 96 · Answer 11 · 2026-04-16 14:09:41

96

Views

How to impose the boundary conditions on $u(x,t)=\int_{-\infty}^{\infty} dk\left[A(k)e^{ik(x-ct)}+B(k)e^{ik(x+ct)}\right]$?

Published on 16 Apr 2026 - 14:09

score 33 · Answer 12 · 2026-04-11 19:50:35

33

Views

Convolution of two monochromatic waves

Published on 11 Apr 2026 - 19:50

score 146 · Answer 13 · 2026-04-11 01:33:59

146

Views

Fourier-transform of a delta-function of a square of the space-time interval

Published on 11 Apr 2026 - 1:33

score 63 · Answer 14 · 2026-04-14 14:04:41

63

Views

Why is a Laplace transform with unfixed contour a good Ansatz to solve Bessel's differential equation? In which situations is this a good Ansatz?

Published on 14 Apr 2026 - 14:04

score 980 · Answer 15 · 2026-04-24 16:11:31

980

Views

Rigorously, why do the Laplace and Fourier transforms “reveal” the sinusoidal or exponential decomposition at their peaks?

Published on 24 Apr 2026 - 16:11

List Question

A problem arises when computing the integral of the sinc function using the Fourier transform.

$f_n(t)=\int_{-n}^{n} \frac{\sin x}{x}\cdot e^{-itx}\ dx$ converges uniformly near $t=0$.

Please Help: Derivative of a sinc function.

Fourier transform of $ \frac{e^{-|\xi|^2 |t|}}{|\xi|^2} $

Computing the Fourier transform of exponential decay in $\mathbb{R}^2$

Fourier transform of $\exp{\left(irx/\sqrt{1-ix}\right)}/(1-ix)$.

Fourier Transform of $\frac{1}{|x|^2-1}$ in $\mathbb{R}^3$

Computing Fibonacci numbers with generating function

A non-trivial condition on $f$ such that $F: \mathbb{R}^2\to\mathbb{C}: F(x,t)=\int_{\mathbb{R}}f(x,y)e^{-2\pi iyt}dy$ is a continuous function.

2D spatial Fourier transform integral calculation

How to impose the boundary conditions on $u(x,t)=\int_{-\infty}^{\infty} dk\left[A(k)e^{ik(x-ct)}+B(k)e^{ik(x+ct)}\right]$?

Convolution of two monochromatic waves

Fourier-transform of a delta-function of a square of the space-time interval

Why is a Laplace transform with unfixed contour a good Ansatz to solve Bessel's differential equation? In which situations is this a good Ansatz?

Rigorously, why do the Laplace and Fourier transforms “reveal” the sinusoidal or exponential decomposition at their peaks?

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