Question

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

score 214 · Answer 1 · 2026-03-25 21:17:52

214

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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 25 Mar 2026 - 21:17

score 170 · Answer 2 · 2026-03-19 03:36:57

170

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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 19 Mar 2026 - 3:36

score 111 · Answer 3 · 2026-03-24 15:11:52

111

Views

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

Published on 24 Mar 2026 - 15:11

score 334 · Answer 4 · 2026-03-21 19:55:59

334

Views

Sources for specific identities of spherical Bessel functions and spherical harmonics

Published on 21 Mar 2026 - 19:55

score 195 · Answer 5 · 2026-03-20 09:16:40

195

Views

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

Published on 20 Mar 2026 - 9:16

score 81 · Answer 6 · 2026-03-22 11:07:38

81

Views

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

Published on 22 Mar 2026 - 11:07

score 462 · Answer 7 · 2026-03-20 07:51:29

462

Views

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

Published on 20 Mar 2026 - 7:51

score 98 · Answer 8 · 2026-03-22 12:50:08

98

Views

Series involving zeros of Bessel functions

Published on 22 Mar 2026 - 12:50

score 122 · Answer 9 · 2026-03-19 22:12:56

122

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 19 Mar 2026 - 22:12

score 275 · Answer 10 · 2026-03-24 15:30:08

275

Views

Transcendental equation with Bessel function

Published on 24 Mar 2026 - 15:30

score 153 · Answer 11 · 2026-03-20 21:56:56

153

Views

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

Published on 20 Mar 2026 - 21:56

score 185 · Answer 12 · 2026-03-25 17:15:12

185

Views

Apprximation of Bessel Function

Published on 25 Mar 2026 - 17:15

score 452 · Answer 13 · 2026-03-25 17:03:42

452

Views

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

Published on 25 Mar 2026 - 17:03

score 714 · Answer 14 · 2026-03-25 09:23:15

714

Views

Proving integral identity for solution to Bessel equation

Published on 25 Mar 2026 - 9:23

score 1.4k · Answer 15 · 2026-03-22 21:55:58

1.4k

Views

Orthogonality of Bessel function

Published on 22 Mar 2026 - 21:55

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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