Heun Functions and Some of Their Applications in Physics

Understand

Most of the theoretical physics known today is described by using a small number of differential equations.

• For linear systems, different forms of the hypergeometric or the confluent hypergeometric equations often suffice to describe the system studied.
• These equations have power series solutions with simple relations between consecutive coefficients and/ or can be represented in terms of simple integral transforms.
• If the problem is nonlinear, one often uses one form of the Painlev\'{e} equations.