Definition:Hypergeometric Differential Equation/Mistake

Source Work

2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.):

hypergeometric differential equation

Mistake

A second-order differential equation of the form

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

where $a$, $b$ and $c$ are constants.

Correction

There is a minus sign which should be a plus:

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

Sources

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