# Definition:Hypergeometric Differential Equation

## Definition

A hypergeometric differential equation is a second order ODE of the form:

$\displaystyle x \paren {1 - x} \frac {\d^2 y} {\d x^2} + \paren {c - \paren {a + b + 1} x} \frac {\d y} {\d x} - a b y = 0$

where $a$, $b$ and $c$ are complex numbers.

## Also see

• Results about hypergeometric differential equations can be found here.