Question

How to prove $\int_{0}^{\infty} \sqrt{x} J_{0}(x)dx = \sqrt{2} \frac{\Gamma(3/4)}{\Gamma(1/4)}$

score 220 · Answer 1 · 2026-04-29 12:08:14

220

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How to prove $\int_{0}^{\infty} \sqrt{x} J_{0}(x)dx = \sqrt{2} \frac{\Gamma(3/4)}{\Gamma(1/4)}$

Published on 29 Apr 2026 - 12:08

score 177 · Answer 2 · 2026-05-05 02:07:07

177

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What can be said about the series $\sum_{n=1}^{\infty} \left[ \frac{1}{n} - \frac{1}{\sqrt{ n^2 + x^2 }} \right]$

Published on 05 May 2026 - 2:07

score 121 · Answer 3 · 2026-05-07 12:46:36

121

Views

A closed-form of an integral containing Bessel's function

Published on 07 May 2026 - 12:46

score 341 · Answer 4 · 2026-04-30 12:29:37

341

Views

Sources for specific identities of spherical Bessel functions and spherical harmonics

Published on 30 Apr 2026 - 12:29

score 203 · Answer 5 · 2026-05-07 10:11:45

203

Views

The solution to the integral $\int_{0}^{\infty} \log(x) K_{0}(2\sqrt{x})\,dx$

Published on 07 May 2026 - 10:11

score 89 · Answer 6 · 2026-05-01 00:24:42

89

Views

Laplace transform of $t^\mu I_\nu(at)$

Published on 01 May 2026 - 0:24

score 469 · Answer 7 · 2026-05-04 09:42:15

469

Views

Integral of product of Bessel functions of first kind and different order and argument

Published on 04 May 2026 - 9:42

score 106 · Answer 8 · 2026-05-03 04:21:04

106

Views

Series involving zeros of Bessel functions

Published on 03 May 2026 - 4:21

score 131 · Answer 9 · 2026-05-07 10:15:54

131

Views

Finding the kernel of a linear map gotten from a linear map with one kind of bessel function $j_i$ and replacing them with the $y_j$

Published on 07 May 2026 - 10:15

score 282 · Answer 10 · 2026-05-05 02:54:42

282

Views

Transcendental equation with Bessel function

Published on 05 May 2026 - 2:54

score 162 · Answer 11 · 2026-05-05 04:36:23

162

Views

integral of the Bessel function involving power and exponential functions and Airy function

Published on 05 May 2026 - 4:36

score 193 · Answer 12 · 2026-04-29 12:08:26

193

Views

Apprximation of Bessel Function

Published on 29 Apr 2026 - 12:08

score 459 · Answer 13 · 2026-04-29 12:08:24

459

Views

How to compute $\int_{0}^{1}x\sin (bx) J_0\!\!\left(a\sqrt{1-x^2}\right)\!\mathrm dx$?

Published on 29 Apr 2026 - 12:08

score 721 · Answer 14 · 2026-04-29 12:08:30

721

Views

Proving integral identity for solution to Bessel equation

Published on 29 Apr 2026 - 12:08

score 1.4k · Answer 15 · 2026-04-29 12:08:27

1.4k

Views

Orthogonality of Bessel function

Published on 29 Apr 2026 - 12:08

List Question

How to prove $\int_{0}^{\infty} \sqrt{x} J_{0}(x)dx = \sqrt{2} \frac{\Gamma(3/4)}{\Gamma(1/4)}$

What can be said about the series $\sum_{n=1}^{\infty} \left[ \frac{1}{n} - \frac{1}{\sqrt{ n^2 + x^2 }} \right]$

A closed-form of an integral containing Bessel's function

Sources for specific identities of spherical Bessel functions and spherical harmonics

The solution to the integral $\int_{0}^{\infty} \log(x) K_{0}(2\sqrt{x})\,dx$

Laplace transform of $t^\mu I_\nu(at)$

Integral of product of Bessel functions of first kind and different order and argument

Series involving zeros of Bessel functions

Finding the kernel of a linear map gotten from a linear map with one kind of bessel function $j_i$ and replacing them with the $y_j$

Transcendental equation with Bessel function

integral of the Bessel function involving power and exponential functions and Airy function

Apprximation of Bessel Function

How to compute $\int_{0}^{1}x\sin (bx) J_0\!\!\left(a\sqrt{1-x^2}\right)\!\mathrm dx$?

Proving integral identity for solution to Bessel equation

Orthogonality of Bessel function

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