DefinitionBessel functions are a family of solutions to Bessels differential equation with a real or complex order alpha and that are not constant multiples of each other for different values of the argument. They are important in many problems in scienctific and engineering involving wave propagation (like sound, light, eletromagnetic wave), heat conduction, and vibration phenomena, with spherical or cylindric symmetry. Sine waves exhibit a unique property such that they oscillate, and this is why they are common in many areas of mathematical, physical, and engineering descriptions - such as waveforms, diffraction patterns and resonant frequencies. Bessel functions appear in the robust-object of wave acoustics, particularly inside the explanation of round acoustics. Example: In the case of a vibrating circular membrane, Bessel functions are used to describe the radial displacement at a position and time for points on the membrane.
