Consider a second-order ordinary differential equation
 |
If 
and 
remain finite at 
, then 
is called an ordinary point.
If either 
or 
diverges as 
,
then 
is called a singular point. If 
diverges more quickly than 
, so 
approaches infinity
as 
,
or 
diverges more quickly than 
so that 
goes to infinity
as 
,
then 
is called an irregular singularity (or essential
singularity).
