Bessel functions of integer order

Bessel functions of integer order are special mathematical functions that describe how waves or vibrations behave in circular or cylindrical systems, such as vibrations in a drumhead or electromagnetic waves in a fiber. They arise as solutions to a differential equation that models these systems when symmetry makes the problem circular. The "integer order" refers to specific types of these functions, each corresponding to different wave modes. They help scientists and engineers analyze phenomena involving circular geometries, providing essential tools for understanding how waves spread, resonate, or decay within circular structures.