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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
by cshimmin 5y ago
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.
- gus_massa 5y agoYou are right.
- icapybara 5y agoAnd there are many. Zernike polynomials are a common one.
- chillingeffect 5y agoNot a wizard or anything but reading wikipedia: Bessel functions for integer α are also known as cylinder functions or the cylindrical harmonics
- gus_massa 5y agoBessel 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.