Question

Is there a way to compute $\int_0^\infty \frac{\cos (qt) J_1 (qr)}{1+q^2} \, \mathrm{d} q$ provided that $0<t<r$?

score 506 · Answer 1 · 2016-10-05 12:11:36

506

Views

Is there a way to compute $\int_0^\infty \frac{\cos (qt) J_1 (qr)}{1+q^2} \, \mathrm{d} q$ provided that $0<t<r$?

Published on 05 Oct 2016 - 12:11

score 167 · Answer 2 · 2026-03-25 16:20:28

167

Views

Parseval's equality for the Fourier transform

Published on 25 Mar 2026 - 16:20

score 88 · Answer 3 · 2016-10-06 09:41:48

88

Views

Is there a way to transform the following integral equation into a differential equation?

Published on 06 Oct 2016 - 9:41

score 73 · Answer 4 · 2016-10-06 18:02:15

73

Views

How to compute $\int_0^s \frac{r\, \mathrm{d}r}{\sqrt{s^2-r^2}\sqrt{t^2-r^2}}$ if we know that $s<t$?

Published on 06 Oct 2016 - 18:02

score 634 · Answer 5 · 2016-10-07 05:18:44

634

Views

Graphical proof of flat/spread-out Fourier transforms of Gaussian distribution

Published on 07 Oct 2016 - 5:18

score 215 · Answer 6 · 2016-10-07 12:28:26

215

Views

How to obtain an inverse integral transform for $F(q) = \int_0^R \chi(t) \sin qt \, \mathrm{d}t$ provided that $\chi$ is an odd function?

Published on 07 Oct 2016 - 12:28

score 128 · Answer 7 · 2016-10-12 09:19:42

128

Views

How to check analytically that the following integral equations has this solution?

Published on 12 Oct 2016 - 9:19

score 54 · Answer 8 · 2016-10-13 10:38:45

54

Views

What are the assumptions that should be made for the determination of the unknown integration constants in this system of dual integral equations?

Published on 13 Oct 2016 - 10:38

score 26 · Answer 9 · 2016-10-15 18:33:29

26

Views

Which relation between $A$, $B$ and $C$ should be satisfied in order the infinite integral below vanish?

Published on 15 Oct 2016 - 18:33

score 79 · Answer 10 · 2016-10-19 09:38:00

79

Views

How to solve analytically a Volterra integral equation of the first kind with an $\arcsin$ kernel function?

Published on 19 Oct 2016 - 9:38

score 52 · Answer 11 · 2016-11-05 09:22:48

52

Views

A question about Laplace Transform: $\mathcal{L}\{yf(y)\}$

Published on 05 Nov 2016 - 9:22

score 553 · Answer 12 · 2016-11-15 09:16:48

553

Views

Transform Theory Reference Request

Published on 15 Nov 2016 - 9:16

score 219 · Answer 13 · 2016-11-21 03:25:11

219

Views

Compute $\int_{-\infty}^{+\infty}(1+\frac{1}{v^2})\exp(-\frac{u^2}{2\sigma_1^2\sigma_2^2}(\sigma_2v+\frac{\sigma_1}{v})^2)\,dv$

Published on 21 Nov 2016 - 3:25

score 209 · Answer 14 · 2026-03-25 16:08:08

209

Views

Explicit transformation between conjugate harmonic functions: Bäcklund/Hilbert/Riesz transform

Published on 25 Mar 2026 - 16:08

score 67 · Answer 15 · 2016-12-01 13:42:48

67

Views

Can you make a product of kernels?

Published on 01 Dec 2016 - 13:42

List Question

Is there a way to compute $\int_0^\infty \frac{\cos (qt) J_1 (qr)}{1+q^2} \, \mathrm{d} q$ provided that $0<t<r$?

Parseval's equality for the Fourier transform

Is there a way to transform the following integral equation into a differential equation?

How to compute $\int_0^s \frac{r\, \mathrm{d}r}{\sqrt{s^2-r^2}\sqrt{t^2-r^2}}$ if we know that $s<t$?

Graphical proof of flat/spread-out Fourier transforms of Gaussian distribution

How to obtain an inverse integral transform for $F(q) = \int_0^R \chi(t) \sin qt \, \mathrm{d}t$ provided that $\chi$ is an odd function?

How to check analytically that the following integral equations has this solution?

What are the assumptions that should be made for the determination of the unknown integration constants in this system of dual integral equations?

Which relation between $A$, $B$ and $C$ should be satisfied in order the infinite integral below vanish?

How to solve analytically a Volterra integral equation of the first kind with an $\arcsin$ kernel function?

A question about Laplace Transform: $\mathcal{L}\{yf(y)\}$

Transform Theory Reference Request

Compute $\int_{-\infty}^{+\infty}(1+\frac{1}{v^2})\exp(-\frac{u^2}{2\sigma_1^2\sigma_2^2}(\sigma_2v+\frac{\sigma_1}{v})^2)\,dv$

Explicit transformation between conjugate harmonic functions: Bäcklund/Hilbert/Riesz transform

Can you make a product of kernels?

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