Question

How can we prove this identify: $\int_0^{2\pi} \exp(i a\cos(x))\, dx = 2 \pi I_0(a)$

score 94 · Answer 1 · 2020-08-19 02:09:29

94

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How can we prove this identify: $\int_0^{2\pi} \exp(i a\cos(x))\, dx = 2 \pi I_0(a)$

Published on 19 Aug 2020 - 2:09

score 117 · Answer 2 · 2026-03-27 19:52:53

117

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Integral of Bessel functions multiply Legendre polynomials.

Published on 27 Mar 2026 - 19:52

score 150 · Answer 3 · 2020-08-23 07:58:02

150

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What function $f(x)$ would this limit, involving 3 integrals be equal to?

Published on 23 Aug 2020 - 7:58

score 119 · Answer 4 · 2020-08-28 16:11:51

119

Views

General equation related with the "vibrating circular membrane" problem, related with Bessel function of the first kind

Published on 28 Aug 2020 - 16:11

score 541 · Answer 5 · 2020-08-31 14:08:48

541

Views

Non-integer order of Bessel's equation

Published on 31 Aug 2020 - 14:08

score 65 · Answer 6 · 2020-09-05 16:22:30

65

Views

solve $t^{2}u''+tu'+(t^{2}-1)u=0$ using Laplace

Published on 05 Sep 2020 - 16:22

score 1.6k · Answer 7 · 2020-09-06 07:34:09

1.6k

Views

Fourier Transform of Bessel Function

Published on 06 Sep 2020 - 7:34

score 167 · Answer 8 · 2026-03-30 08:37:30

167

Views

How to arrive at this solution to an integral over the Bessel function of the first kind?

Published on 30 Mar 2026 - 8:37

score 280 · Answer 9 · 2020-09-10 11:27:06

280

Views

How to evaluate $\int_0^\infty\lambda\left(I_0(\lambda)K_0(\lambda)-I_1(\lambda)K_1(\lambda)\right)\sin(\lambda z)J_0(\lambda t)\,\mathrm{d}\lambda$?

Published on 10 Sep 2020 - 11:27

score 120 · Answer 10 · 2020-09-16 02:39:43

120

Views

Evaluate a definite integrals given in term of Bessel functions

Published on 16 Sep 2020 - 2:39

score 83 · Answer 11 · 2020-09-17 19:45:11

83

Views

Single modified Bessel function solution to orthogonal partial differential equations

Published on 17 Sep 2020 - 19:45

score 234 · Answer 12 · 2020-09-21 01:21:16

234

Views

Bessel’s equation of order zero , what is zero referring to?

Published on 21 Sep 2020 - 1:21

score 416 · Answer 13 · 2020-09-22 02:44:36

416

Views

Solve: $j_n(ka)=\frac{ka}{n}j_{n-1}(ka)$. Zeros of equation with spherical Bessel functions.

Published on 22 Sep 2020 - 2:44

score 2.5k · Answer 14 · 2020-09-24 19:29:11

2.5k

Views

Proving the Jacobi-Anger Expansion

Published on 24 Sep 2020 - 19:29

score 101 · Answer 15 · 2026-03-28 10:55:37

101

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Solving for Eigenvalues of Bessel like differential equations

Published on 28 Mar 2026 - 10:55

List Question

How can we prove this identify: $\int_0^{2\pi} \exp(i a\cos(x))\, dx = 2 \pi I_0(a)$

Integral of Bessel functions multiply Legendre polynomials.

What function $f(x)$ would this limit, involving 3 integrals be equal to?

General equation related with the "vibrating circular membrane" problem, related with Bessel function of the first kind

Non-integer order of Bessel's equation

solve $t^{2}u''+tu'+(t^{2}-1)u=0$ using Laplace

Fourier Transform of Bessel Function

How to arrive at this solution to an integral over the Bessel function of the first kind?

How to evaluate $\int_0^\infty\lambda\left(I_0(\lambda)K_0(\lambda)-I_1(\lambda)K_1(\lambda)\right)\sin(\lambda z)J_0(\lambda t)\,\mathrm{d}\lambda$?

Evaluate a definite integrals given in term of Bessel functions

Single modified Bessel function solution to orthogonal partial differential equations

Bessel’s equation of order zero , what is zero referring to?

Solve: $j_n(ka)=\frac{ka}{n}j_{n-1}(ka)$. Zeros of equation with spherical Bessel functions.

Proving the Jacobi-Anger Expansion

Solving for Eigenvalues of Bessel like differential equations

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