Bessel function

The most useful definition really is related to the Fourier transform of radial functions.

The wikipedia definition is here.

Fourier transforms of spherical distributions

If \(f = \delta_R\) as a radial function (that is, \(f\) is a Dirac mass on the sphere of radius \(R\)), then we get from the Fourier transform of radial functions \[\begin{align} \hat{f(t)}=2 \pi \| t\|^{-\alpha}J_{\alpha}(2 \pi R \| t\|)R^{\alpha + 1} .\end{align}\]

This makes Bessel functions analogous to Kravchuk polynomials.