ABSTRACT
Bessel functions come up in many calculations in physics. When one separates variables in the Helmholtz equation in cylindrical or spherical coordinates the radial equation is Bessel's equation or can be reduced to Bessel's equation. Many important integrals, for example, can be expressed in terms of them. In fact, Bessel functions are similar in many respects to trigonometric functions and it is necessary to have a working knowledge of them for the same sorts of reasons that it is necessary to have a working knowledge of trigonometric functions. Bessel functions of imaginary argument often occur in practice and have special names and symbols. There are cylindrical analogues to the electrostatic and hydrodynamic examples.
