ABSTRACT
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. Bessel functions come up in many calculations in physics. 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. The quantity on the left is thus a generating function for the Bessel functions of integral order.
