List questions from bessel-functions

Published on 25 Dec 2020 - 13:06

113

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$J_n(z)=(z/2)^n\frac{1}{\pi(\frac{1}{2})_n}\int_{0}^{\pi}\cos(z\cos\theta)\sin^{2n}\theta d\theta$

Published on 26 Dec 2020 - 14:29

68

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Find $\int\limits_0^\infty {x{e^{ - (a{x^2} + b)}}{I_0}\left( {\sqrt {c{x^2} + dx + k} } \right)dx} $?

Published on 23 Feb 2026 - 14:09

802

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separation of variables to find solution to heat equation (cylinder)

Published on 05 Jan 2021 - 6:17

729

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1F2 Hypergeometric and Bessel function

Published on 09 Jan 2021 - 8:29

64

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$\int_{0}^{\pi} \! \frac{\sin \sqrt{x + y \cos\phi}}{\sqrt{x + y \cos\phi}} \, d\phi$

Published on 09 Jan 2021 - 15:48

150

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How can you solve this Bessel's equation?

Published on 10 Jan 2021 - 17:54

60

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Separating real and imaginary parts from a plane wave expansion

Published on 10 Jan 2021 - 21:55

84

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Integral of a modified Bessel function of the second kind 1st order

Published on 11 Jan 2021 - 6:23

83

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Integral representation of the nth power of the zeroth Bessel function?

Published on 13 Jan 2021 - 4:05

83

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Compute $\int_0^\infty x^{n+1} J_n(kx) \exp(-a^2 x^2) dx$

Published on 13 Jan 2021 - 9:23

495

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The Fourier Transform of a Bessel function: $J_a(be^{-x}), a,b>0$

Published on 14 Jan 2021 - 14:20

105

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Condition on Bessel function to be bounded

Published on 02 Apr 2026 - 10:13

266

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How do I calculate the double integral of a Hankel function?

Published on 14 Jan 2021 - 18:04

193

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Expansion of a modified Struve function in terms of modified Bessel functions

Published on 14 Jan 2021 - 19:18

List Question

Why does the ODE $xy''+y'+xy=0$ require only one initial condition?

$J_n(z)=(z/2)^n\frac{1}{\pi(\frac{1}{2})_n}\int_{0}^{\pi}\cos(z\cos\theta)\sin^{2n}\theta d\theta$

Find $\int\limits_0^\infty {x{e^{ - (a{x^2} + b)}}{I_0}\left( {\sqrt {c{x^2} + dx + k} } \right)dx} $?

separation of variables to find solution to heat equation (cylinder)

1F2 Hypergeometric and Bessel function

$\int_{0}^{\pi} \! \frac{\sin \sqrt{x + y \cos\phi}}{\sqrt{x + y \cos\phi}} \, d\phi$

How can you solve this Bessel's equation?

Separating real and imaginary parts from a plane wave expansion

Integral of a modified Bessel function of the second kind 1st order

Integral representation of the nth power of the zeroth Bessel function?

Compute $\int_0^\infty x^{n+1} J_n(kx) \exp(-a^2 x^2) dx$

The Fourier Transform of a Bessel function: $J_a(be^{-x}), a,b>0$

Condition on Bessel function to be bounded

How do I calculate the double integral of a Hankel function?

Expansion of a modified Struve function in terms of modified Bessel functions

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