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Bessel Functions

Bessel Functions. Bessel functions , are canonical  solutions  y ( x ) of  Bessel's  differential equation :. α (the  order  of the Bessel function).

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Bessel Functions

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  1. Bessel Functions Bessel functions, arecanonical solutions y(x) of Bessel's differential equation: α (the order of the Bessel function) Bessel functions are also known as cylinder functions or cylindrical harmonics because they are found in the solution to Laplace's equation in cylindrical coordinates.

  2. Applications of Bessel functions • Electromagnetic waves in a cylindrical waveguide • Heat conduction in a cylindrical object • Modes of vibration of a thin circular (or annular) artificial membrane (such as a drum or other membranophone) • Diffusion problems on a lattice • Solutions to the radial Schrödinger equation (in spherical and cylindrical coordinates) for a free particle • Solving for patterns of acoustical radiation • Frequency-dependent friction in circular pipelines

  3. Bessel functions of the first kind : Jα

  4. Bessel functions of the second kind  : Yα

  5. Circular membrane

  6. Modified Bessel Equation

  7. Modified Bessel functions : Iα, Kα

  8. Modified Bessel functions : Iα, Kα

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