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).

**References**

Arfken, G. ``Singular Points.'' §8.4 in *Mathematical Methods for Physicists, 3rd ed.*
Orlando, FL: Academic Press, pp. 451-454, 1985.

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1999-05-26