X-Nico

Abel's identity

It is especially useful for equations such as Bessel's equation where the solutions do not have a simple analytical form, because in such cases the Wronskian is difficult to compute directly.

Bessel function

This differential equation, and the Riccati–Bessel solutions, arises in the problem of scattering of electromagnetic waves by a sphere, known as Mie scattering after the first published solution by Mie (1908).

Cylindrical harmonics

where $I\; n(z)$ and $K\; n(z)$ are modified Bessel functions.

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The term cylindrical harmonics is also used to refer to the Bessel functions (that are cylindrical harmonics in the sense described above).

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where $J\; n(z)$ and $Y\; n(z)$ are ordinary Bessel functions.

Vibrations of a circular membrane

Going back to the equation for $R(r),$ its solution is a linear combination of Bessel functions $J\; m$ and $Y\; m.$

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Turning to the equation for $R(r),$ with the observation that $K=-\backslash lambda^2,$ all solutions of this second-order differential equation are a linear combination of Bessel functions of order 0,

Wu–Sprung potential

For the case of the Riemann zeros Wu and Sprung and others have shown that the potential can be written implicitly in terms of the Gamma function and zeroth-order Bessel function.

see also