Definition:Hypergeometic Differential Equation

Definition

A hypergeometic differential equation s a second order differential equation in the form:

$x \paren {1 - x} \dfrac {\d^2 \phi} {\d x^2} + \paren {c - \paren {a + b - 1} } \dfrac {\d \phi} {\d x} - a b \phi = 0$

where $a, b, c \in \R$ are constants.

Also see

• Results about hypergeometic differential equations can be found here.

Sources

• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): hypergeometic differential equation
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): hypergeometic differential equation