Re:Circular Harmonics
by cshimmin on Friday October 29, 2021 @08:07PM
(#29044878)
Not really. In Mathematics "circle" refers to a boundary of a disk. So it's a 1D periodic manifold, and the circular harmonics/Fourier series are the basis for such periodic functions. The bessel functions give a basis for the radial part of 2D solutions to a certain class of differential equations on a 2D disk. Incidentally the radial part of those solutions are circular harmonics.
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And there are many. Zernike polynomials are a common one.
Re:Circular Harmonics
by chillingeffect on Friday October 29, 2021 @09:34PM
(#29045269)
Not a wizard or anything but reading wikipedia:
Bessel functions for integer α are also known as cylinder functions or the cylindrical harmonics
Bessel functions are useful when you must solve the volume of the cylinder (or the volume outside a cylinder). If you only care about the surface of the cylinder, you must use the Fourier series in one direction and the Fourier transform in the other direction.
I (GGP comment) was wrong.