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).

**References**

Arfken, G. ``Singular Points.'' §8.4 in *Mathematical Methods for Physicists, 3rd ed.* Orlando, FL: Academic Press,
pp. 451-453 and 461-463, 1985.

© 1996-9

1999-05-26