## The Bessel and Struve functions

**Bessel** functions are both of the canonical solutions to Bessel's homogeneous differential equation:

These equations arise naturally in the solution of Laplace's equation in cylindrical coordinates. The solutions of the non-homogeneous Bessel differential equation shown in the following diagram are called **Struve** functions:

In either case, the order of the equation is the complex number `alpha`

which acts as a parameter. Depending on the canonical solution and the order, the Bessel and Struve functions are addressed (and computed) differently.

For Bessel functions, we have algorithms to produce Bessel functions of the first kind (`jv`

) and second kind (`yn`

and `yv`

), Hankel functions of the first and second kind (`hankel1`

and `hankel2`

), and the modified Bessel functions of the first and second kind (`iv`

, `kn`

, and `kv`

). Their syntax is similar in all cases: first parameter is the order and second parameter the independent variable. The component *n* in the definition indicates...