New solutions of Heun general equation

Understand

We show that in four particular cases the derivative of the solution of Heun general equation can be expressed in terms of a solution to another Heun equation.

• Starting from this property, we use the Gauss hypergeometric functions to construct series solutions to Heun equation for the mentioned cases.
• Each of the hypergeometric functions involved has correct singular behavior at only one of the singular points of the equation; the sum, however, has correct behavior.