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...