\begin{definition}[Definition:Hypergeometric Differential Equation]
A '''hypergeometric differential equation''' is a second order ODE of the form:
:$x \paren {1 - x} \dfrac {\d^2 y} {\d x^2} + \paren {c - \paren {a + b + 1} x} \dfrac {\d y} {\d x} - a b y = 0$
where $a$, $b$ and $c$ are complex numbers.
\end{definition}