Question

Inverse Fourier Transform involving Bessel function

score 229 · Answer 1 · 2021-11-24 07:59:12

229

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Inverse Fourier Transform involving Bessel function

Published on 24 Nov 2021 - 7:59

score 619 · Answer 2 · 2026-03-26 04:16:14

619

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Integral representation of Bessel function $J_1(x)$

Published on 26 Mar 2026 - 4:16

score 229 · Answer 3 · 2026-03-28 08:09:52

229

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How to relate $\int_{-1}^{1}e^{ikru} P_{\ell}(u)du$ to $j_\ell(kr)$ in a simple way?

Published on 28 Mar 2026 - 8:09

score 124 · Answer 4 · 2021-11-26 15:02:39

124

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Limit of integral with a Bessel function

Published on 26 Nov 2021 - 15:02

score 164 · Answer 5 · 2021-11-26 20:15:17

164

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Asymptotic Expansion of the Bessel-Integral Function

Published on 26 Nov 2021 - 20:15

score 47 · Answer 6 · 2021-11-27 08:37:54

47

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Expansion of $\exp(\text{-constant}\times x)$ in terms of modified Bessel function

Published on 27 Nov 2021 - 8:37

score 106 · Answer 7 · 2021-11-29 01:01:06

106

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Asymptotic answer of Fourier transform radially symmetric function with a ring of minimum

Published on 29 Nov 2021 - 1:01

score 66 · Answer 8 · 2021-12-01 01:46:23

66

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Finding the Bessel function for Hankel transform

Published on 01 Dec 2021 - 1:46

score 56 · Answer 9 · 2021-12-03 02:29:18

56

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How to evaluate the Fourier Series of $\frac{\sin(\alpha\sin(\omega t))}{\alpha\sin(\omega t)}\exp(-j\beta\sin(\omega t))$?

Published on 03 Dec 2021 - 2:29

score 79 · Answer 10 · 2021-12-06 08:34:46

Can $ I_n(z) = (\frac{z}{2})^n\sum_{k=0}^\infty\frac{(-1)^k}{k!(n+k)!}\frac{1}{k+(n+k)+1}(\frac{z}{2})^{2k}$ be expressed by the Bessel function?

score 81 · Answer 11 · 2021-12-09 09:39:25

81

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Interval of convergence for the Laplace transform of $J_0(t)$

Published on 09 Dec 2021 - 9:39

score 57 · Answer 12 · 2021-12-09 10:37:26

57

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Integral with modified Bessel function of the first kind with hyperbolic function

Published on 09 Dec 2021 - 10:37

score 90 · Answer 13 · 2021-12-10 14:37:02

90

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For $a>0$, what is $\int_1^\infty dy \, \exp(-ay) (y^2-1)^{-1/2}y^{-2}$?

Published on 10 Dec 2021 - 14:37

score 242 · Answer 14 · 2021-12-13 14:40:13

242

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Prove that $ \sum_{k=0}^n \frac{(-1)^k}{k!}\binom{n}{k}=e\int_0^\infty \frac{t^ne^{-t}}{n!} J_0(2\sqrt{t})\;\mathrm{d}t$ using only real analysis.

Published on 13 Dec 2021 - 14:40

score 42 · Answer 15 · 2026-04-01 09:32:42

42

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Orthogonality relation of $e^{i\vec k \cdot \vec x} $: how to pass from cartesian to spherical coordinates

Published on 01 Apr 2026 - 9:32

List Question

Inverse Fourier Transform involving Bessel function

Integral representation of Bessel function $J_1(x)$

How to relate $\int_{-1}^{1}e^{ikru} P_{\ell}(u)du$ to $j_\ell(kr)$ in a simple way?

Limit of integral with a Bessel function

Asymptotic Expansion of the Bessel-Integral Function

Expansion of $\exp(\text{-constant}\times x)$ in terms of modified Bessel function

Asymptotic answer of Fourier transform radially symmetric function with a ring of minimum

Finding the Bessel function for Hankel transform

How to evaluate the Fourier Series of $\frac{\sin(\alpha\sin(\omega t))}{\alpha\sin(\omega t)}\exp(-j\beta\sin(\omega t))$?

Can $ I_n(z) = (\frac{z}{2})^n\sum_{k=0}^\infty\frac{(-1)^k}{k!(n+k)!}\frac{1}{k+(n+k)+1}(\frac{z}{2})^{2k}$ be expressed by the Bessel function?

Interval of convergence for the Laplace transform of $J_0(t)$

Integral with modified Bessel function of the first kind with hyperbolic function

For $a>0$, what is $\int_1^\infty dy \, \exp(-ay) (y^2-1)^{-1/2}y^{-2}$?

Prove that $ \sum_{k=0}^n \frac{(-1)^k}{k!}\binom{n}{k}=e\int_0^\infty \frac{t^ne^{-t}}{n!} J_0(2\sqrt{t})\;\mathrm{d}t$ using only real analysis.

Orthogonality relation of $e^{i\vec k \cdot \vec x} $: how to pass from cartesian to spherical coordinates

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