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