Question

$\int_0^\infty J_0(ax)e^{-px} dx=\frac{1}{\sqrt{a^2+p^2}}$ without using Laplace transform tables

score 208 · Answer 1 · 2017-08-26 12:14:14

208

Views

$\int_0^\infty J_0(ax)e^{-px} dx=\frac{1}{\sqrt{a^2+p^2}}$ without using Laplace transform tables

Published on 26 Aug 2017 - 12:14

score 38 · Answer 2 · 2017-08-26 16:16:57

38

Views

Under which conditions this infinite integral involving a product of an exponential and a zeroth order Bessel function exists?

Published on 26 Aug 2017 - 16:16

score 53 · Answer 3 · 2017-08-27 07:49:03

53

Views

Why is $\sum_{n\geq 0}\frac{(-1)^n}{4^n p^{2n+1}}\binom{2n}{n}=\frac{1}{p}\sum_{n\geq 0}\binom{-1/2}{n}\frac{1}{p^{2n}} $ true?

Published on 27 Aug 2017 - 7:49

score 101 · Answer 4 · 2017-08-28 17:37:10

101

Views

Integral with exponential (or K-Bessel function) depending on a parameter equal to zero?

Published on 28 Aug 2017 - 17:37

score 139 · Answer 5 · 2026-03-26 06:01:38

139

Views

Why is the electric field of a naturally equilibrating, isotropic, cylindrical conductor not a function of z (height)?

Published on 26 Mar 2026 - 6:01

score 428 · Answer 6 · 2017-09-06 04:46:04

428

Views

Evaluating the Gamma function in Bessel's equation

Published on 06 Sep 2017 - 4:46

score 376 · Answer 7 · 2017-09-06 08:33:06

376

Views

Have these bounds on Bessel function root spacing been proven?

Published on 06 Sep 2017 - 8:33

score 124 · Answer 8 · 2017-09-07 06:03:36

124

Views

First-kind Bessel function

Published on 07 Sep 2017 - 6:03

score 3.5k · Answer 9 · 2017-09-08 21:55:58

3.5k

Views

Fourier transform of modified Bessel function of the second kind

Published on 08 Sep 2017 - 21:55

score 488 · Answer 10 · 2017-09-11 18:49:19

488

Views

Sum of modified Bessel functions of the second kind

Published on 11 Sep 2017 - 18:49

score 1k · Answer 11 · 2017-09-16 04:19:54

1k

Views

Solve the Bessel Equation to show it satisfies the differential equation

Published on 16 Sep 2017 - 4:19

score 76 · Answer 12 · 2026-03-29 22:31:38

76

Views

Monotonicity of a sequence $\frac{(\mu/2)^n}{n!}K_{n-\frac{1}{2}}(\mu)$

Published on 29 Mar 2026 - 22:31

score 82 · Answer 13 · 2017-09-24 01:58:37

82

Views

How to get rid of imaginary values that come from Bessel $\ K_n (-x)$??

Published on 24 Sep 2017 - 1:58

score 436 · Answer 14 · 2026-03-30 10:44:16

436

Views

Coupled modified Bessel differential equations

Published on 30 Mar 2026 - 10:44

score 491 · Answer 15 · 2017-09-30 19:10:04

491

Views

How to evaluate $\int_{0}^{\infty} e^{ - a x } \sinh(\pi x) K_{ix}(b) K_{ix}(c) dx$?

Published on 30 Sep 2017 - 19:10

List Question

$\int_0^\infty J_0(ax)e^{-px} dx=\frac{1}{\sqrt{a^2+p^2}}$ without using Laplace transform tables

Under which conditions this infinite integral involving a product of an exponential and a zeroth order Bessel function exists?

Why is $\sum_{n\geq 0}\frac{(-1)^n}{4^n p^{2n+1}}\binom{2n}{n}=\frac{1}{p}\sum_{n\geq 0}\binom{-1/2}{n}\frac{1}{p^{2n}} $ true?

Integral with exponential (or K-Bessel function) depending on a parameter equal to zero?

Why is the electric field of a naturally equilibrating, isotropic, cylindrical conductor not a function of z (height)?

Evaluating the Gamma function in Bessel's equation

Have these bounds on Bessel function root spacing been proven?

First-kind Bessel function

Fourier transform of modified Bessel function of the second kind

Sum of modified Bessel functions of the second kind

Solve the Bessel Equation to show it satisfies the differential equation

Monotonicity of a sequence $\frac{(\mu/2)^n}{n!}K_{n-\frac{1}{2}}(\mu)$

How to get rid of imaginary values that come from Bessel $\ K_n (-x)$??

Coupled modified Bessel differential equations

How to evaluate $\int_{0}^{\infty} e^{ - a x } \sinh(\pi x) K_{ix}(b) K_{ix}(c) dx$?

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