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. Singular points are further
classified as follows:
- 1. If either
or
diverges as
but
and
remain Finite
as
, then
is called a Regular Singular Point (or Nonessential Singularity).
- 2. 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).
See also Irregular Singularity, Regular Singular Point, Singularity
References
Arfken, G. ``Singular Points.'' §8.4 in Mathematical Methods for Physicists, 3rd ed.
Orlando, FL: Academic Press, pp. 451-454, 1985.
© 1996-9 Eric W. Weisstein
1999-05-26